diff --git a/dvc/repo/experiments/exceptions.py b/dvc/repo/experiments/exceptions.py
--- a/dvc/repo/experiments/exceptions.py
+++ b/dvc/repo/experiments/exceptions.py
@@ -25,13 +25,13 @@ def __init__(self, rev, expected):
 
 
 class ExperimentExistsError(DvcException):
-    def __init__(self, name: str):
+    def __init__(self, name: str, command: str = "run"):
         msg = (
             "Experiment conflicts with existing experiment "
             f"'{name}'. To overwrite the existing experiment run:\n\n"
-            "\tdvc exp run -f ...\n\n"
-            "To run this experiment with a different name run:\n\n"
-            f"\tdvc exp run -n <new_name> ...\n"
+            f"\tdvc exp {command} -f ...\n\n"
+            f"To {command} this experiment with a different name run:\n\n"
+            f"\tdvc exp {command} -n <new_name> ...\n"
         )
         super().__init__(msg)
         self.name = name
diff --git a/dvc/repo/experiments/executor/local.py b/dvc/repo/experiments/executor/local.py
--- a/dvc/repo/experiments/executor/local.py
+++ b/dvc/repo/experiments/executor/local.py
@@ -2,13 +2,12 @@
 import os
 from contextlib import ExitStack
 from tempfile import mkdtemp
-from typing import TYPE_CHECKING, List, Optional
+from typing import TYPE_CHECKING, Optional
 
 from funcy import cached_property, retry
 from scmrepo.exceptions import SCMError as _SCMError
 from shortuuid import uuid
 
-from dvc.exceptions import DvcException
 from dvc.lock import LockError
 from dvc.scm import SCM, GitMergeError
 from dvc.utils.fs import makedirs, remove
@@ -25,7 +24,7 @@
     ExpRefInfo,
 )
 from ..utils import EXEC_TMP_DIR, get_exp_rwlock
-from .base import BaseExecutor, ExecutorResult, TaskStatus
+from .base import BaseExecutor, TaskStatus
 
 if TYPE_CHECKING:
     from scmrepo.git import Git
@@ -33,7 +32,6 @@
     from dvc.repo import Repo
 
     from ..stash import ExpStashEntry
-    from .base import ExecutorInfo
 
 logger = logging.getLogger(__name__)
 
@@ -249,57 +247,3 @@ def cleanup(self, infofile: str):
             checkpoint = self.scm.get_ref(EXEC_CHECKPOINT)
             if checkpoint and checkpoint != self._orig_checkpoint:
                 self.scm.set_ref(EXEC_APPLY, checkpoint)
-
-    @classmethod
-    def save(
-        cls,
-        info: "ExecutorInfo",
-        force: bool = False,
-        include_untracked: Optional[List[str]] = None,
-    ) -> ExecutorResult:
-        from dvc.repo import Repo
-
-        exp_hash: Optional[str] = None
-        exp_ref: Optional[ExpRefInfo] = None
-
-        dvc = Repo(os.path.join(info.root_dir, info.dvc_dir))
-        old_cwd = os.getcwd()
-        if info.wdir:
-            os.chdir(os.path.join(dvc.scm.root_dir, info.wdir))
-        else:
-            os.chdir(dvc.root_dir)
-
-        try:
-            stages = dvc.commit([], force=force)
-            exp_hash = cls.hash_exp(stages)
-            if include_untracked:
-                dvc.scm.add(include_untracked)
-            cls.commit(
-                dvc.scm,
-                exp_hash,
-                exp_name=info.name,
-                force=force,
-            )
-            ref: Optional[str] = dvc.scm.get_ref(EXEC_BRANCH, follow=False)
-            exp_ref = ExpRefInfo.from_ref(ref) if ref else None
-            untracked = dvc.scm.untracked_files()
-            if untracked:
-                logger.warning(
-                    "The following untracked files were present in "
-                    "the workspace before saving but "
-                    "will not be included in the experiment commit:\n"
-                    "\t%s",
-                    ", ".join(untracked),
-                )
-            info.result_hash = exp_hash
-            info.result_ref = ref
-            info.result_force = False
-            info.status = TaskStatus.SUCCESS
-        except DvcException:
-            info.status = TaskStatus.FAILED
-            raise
-        finally:
-            dvc.close()
-            os.chdir(old_cwd)
-
-        return ExecutorResult(ref, exp_ref, info.result_force)
diff --git a/dvc/repo/experiments/save.py b/dvc/repo/experiments/save.py
--- a/dvc/repo/experiments/save.py
+++ b/dvc/repo/experiments/save.py
@@ -2,7 +2,9 @@
 import os
 from typing import TYPE_CHECKING, List, Optional
 
-from funcy import first
+from .exceptions import ExperimentExistsError, UnchangedExperimentError
+from .refs import ExpRefInfo
+from .utils import check_ref_format, get_random_exp_name
 
 if TYPE_CHECKING:
     from dvc.repo import Repo
@@ -11,6 +13,32 @@
 logger = logging.getLogger(__name__)
 
 
+def _save_experiment(
+    repo: "Repo",
+    baseline_rev: str,
+    force: bool,
+    name: Optional[str],
+    include_untracked: Optional[List[str]],
+) -> str:
+    repo.commit([], force=True)
+
+    name = name or get_random_exp_name(repo.scm, baseline_rev)
+    ref_info = ExpRefInfo(baseline_rev, name)
+    check_ref_format(repo.scm.dulwich, ref_info)
+    ref = str(ref_info)
+    if repo.scm.get_ref(ref) and not force:
+        raise ExperimentExistsError(ref_info.name, command="save")
+
+    repo.scm.add([], update=True)
+    if include_untracked:
+        repo.scm.add(include_untracked)
+    repo.scm.commit(f"dvc: commit experiment {name}", no_verify=True)
+    exp_rev = repo.scm.get_rev()
+    repo.scm.set_ref(ref, exp_rev, old_ref=None)
+
+    return exp_rev
+
+
 def save(
     repo: "Repo",
     name: Optional[str] = None,
@@ -21,24 +49,35 @@ def save(
 
     Returns the saved experiment's SHAs.
     """
-    queue = repo.experiments.workspace_queue
     logger.debug("Saving workspace in %s", os.getcwd())
 
-    staged, _, _ = repo.scm.status(untracked_files="no")
-    if staged:
+    _, _, untracked = repo.scm.status()
+    if include_untracked:
+        untracked = [
+            file for file in untracked if file not in include_untracked
+        ]
+    if untracked:
         logger.warning(
-            "Your workspace contains staged Git changes which will be "
-            "unstaged before saving this experiment."
+            "The following untracked files were present in "
+            "the workspace before saving but "
+            "will not be included in the experiment commit:\n"
+            "\t%s",
+            ", ".join(untracked),
         )
-        repo.scm.reset()
 
-    entry = repo.experiments.new(queue=queue, name=name, force=force)
-    executor = queue.init_executor(repo.experiments, entry)
+    with repo.scm.detach_head(client="dvc") as orig_head:
+        with repo.scm.stash_workspace() as workspace:
+            try:
+                if workspace is not None:
+                    repo.scm.stash.apply(workspace)
+                else:
+                    if not (include_untracked or force):
+                        raise UnchangedExperimentError(orig_head)
 
-    save_result = executor.save(
-        executor.info, force=force, include_untracked=include_untracked
-    )
-    result = queue.collect_executor(repo.experiments, executor, save_result)
+                exp_rev = _save_experiment(
+                    repo, orig_head, force, name, include_untracked
+                )
+            finally:
+                repo.scm.reset(hard=True)
 
-    exp_rev = first(result)
     return exp_rev

> should not contain the extra .dvc/tmp/repro.dat, which is just used for dvc exp run to pass repro arguments.

We should probably not generate that file (add an option to skip?) when calling ` _stash_exp` from `experiments.save`
diff --git a/tests/func/experiments/test_save.py b/tests/func/experiments/test_save.py
--- a/tests/func/experiments/test_save.py
+++ b/tests/func/experiments/test_save.py
@@ -1,16 +1,31 @@
-from contextlib import nullcontext
-
 import pytest
 from funcy import first
 
-from dvc.repo.experiments.exceptions import ExperimentExistsError
+from dvc.repo.experiments.exceptions import (
+    ExperimentExistsError,
+    InvalidArgumentError,
+    UnchangedExperimentError,
+)
 from dvc.repo.experiments.utils import exp_refs_by_rev
 from dvc.scm import resolve_rev
-from dvc.stage.exceptions import StageCommitError
+
+
+@pytest.fixture
+def modified_exp_stage(exp_stage, tmp_dir):
+    with open(tmp_dir / "copy.py", "a", encoding="utf-8") as fh:
+        fh.write("\n# dummy change")
+    yield
+
+
+def test_exp_save_unchanged(tmp_dir, dvc, scm, exp_stage):
+    with pytest.raises(UnchangedExperimentError):
+        dvc.experiments.save()
+
+    dvc.experiments.save(force=True)
 
 
 @pytest.mark.parametrize("name", (None, "test"))
-def test_exp_save(tmp_dir, dvc, scm, exp_stage, name):
+def test_exp_save(tmp_dir, dvc, scm, exp_stage, name, modified_exp_stage):
     baseline = scm.get_rev()
 
     exp = dvc.experiments.save(name=name)
@@ -22,39 +37,39 @@ def test_exp_save(tmp_dir, dvc, scm, exp_stage, name):
     assert resolve_rev(scm, exp_name) == exp
 
 
-@pytest.mark.parametrize(
-    ("force", "expected_raises"),
-    (
-        (False, pytest.raises(StageCommitError)),
-        (True, nullcontext()),
-    ),
-)
-def test_exp_save_force(tmp_dir, dvc, scm, exp_stage, force, expected_raises):
-    with open(tmp_dir / "copy.py", "a", encoding="utf-8") as fh:
-        fh.write("\n# dummy change")
-
-    with expected_raises:
-        dvc.experiments.save(force=force)
+def test_exp_save_overwrite_experiment(
+    tmp_dir, dvc, scm, exp_stage, modified_exp_stage
+):
+    name = "dummy"
+    dvc.experiments.save(name=name)
 
+    with pytest.raises(ExperimentExistsError):
+        dvc.experiments.save(name=name)
 
-def test_exp_save_overwrite_experiment(tmp_dir, dvc, scm, exp_stage):
-    dvc.experiments.save(name="dummy")
-
-    with open(tmp_dir / "copy.py", "a", encoding="utf-8") as fh:
-        fh.write("\n# dummy change")
+    dvc.experiments.save(name=name, force=True)
 
-    with pytest.raises(ExperimentExistsError):
-        dvc.experiments.save(name="dummy")
 
-    dvc.experiments.save(name="dummy", force=True)
+@pytest.mark.parametrize(
+    "name",
+    (
+        "invalid/name",
+        "invalid..name",
+        "invalid~name",
+        "invalid?name",
+        "invalidname.",
+    ),
+)
+def test_exp_save_invalid_name(tmp_dir, dvc, scm, exp_stage, name):
+    with pytest.raises(InvalidArgumentError):
+        dvc.experiments.save(name=name, force=True)
 
 
 def test_exp_save_after_commit(tmp_dir, dvc, scm, exp_stage):
     baseline = scm.get_rev()
-    dvc.experiments.save(name="exp-1")
+    dvc.experiments.save(name="exp-1", force=True)
 
     tmp_dir.scm_gen({"new_file": "new_file"}, commit="new baseline")
-    dvc.experiments.save(name="exp-2")
+    dvc.experiments.save(name="exp-2", force=True)
 
     all_exps = dvc.experiments.ls(all_commits=True)
     assert all_exps[baseline[:7]] == ["exp-1"]
diff --git a/tests/unit/repo/experiments/test_utils.py b/tests/unit/repo/experiments/test_utils.py
--- a/tests/unit/repo/experiments/test_utils.py
+++ b/tests/unit/repo/experiments/test_utils.py
@@ -32,7 +32,19 @@ def test_resolve_exp_ref(tmp_dir, scm, git_upstream, name_only, use_url):
 
 
 @pytest.mark.parametrize(
-    "name,result", [("name", True), ("group/name", False), ("na me", False)]
+    "name,result",
+    [
+        ("name", True),
+        ("group/name", False),
+        ("na me", False),
+        ("invalid/.name", False),
+        ("@", pytest.param(False, marks=pytest.mark.xfail)),
+        (":", False),
+        ("^", False),
+        ("*", False),
+        ("~", False),
+        ("?", False),
+    ],
 )
 def test_run_check_ref_format(scm, name, result):
 

exp branch: includes extra files when used with exp save
# Bug Report

## exp branch: includes extra files when used with exp save

## Description
When creating a branch from an experiment saved with `dvc exp save`, an extra file (`.dvc/tmp/repro.dat`) is commited.


### Reproduce
```bash
cd $(mktemp -d)
git init
dvc init
git commit -m "dvc init"
dvc exp save -n expname
dvc exp branch expname branchname
git show branchname # includes `.dvc/tmp/repro.dat`
```
### Expected

In the case when the workspace is clean, an error should be returned (nothing changed in the experiment). When modified files are present or untracked files are included, the experiment should succeed but should not contain the extra `.dvc/tmp/repro.dat`, which is just used for `dvc exp run` to pass repro arguments.


tests/func/experiments/test_save.py::test_exp_save_unchanged tests/func/experiments/test_save.py::test_exp_save[None] tests/func/experiments/test_save.py::test_exp_save[test] tests/func/experiments/test_save.py::test_exp_save_overwrite_experiment
tests/func/experiments/test_save.py::test_exp_save_invalid_name[invalid/name] tests/func/experiments/test_save.py::test_exp_save_invalid_name[invalid..name] tests/func/experiments/test_save.py::test_exp_save_invalid_name[invalid~name] tests/func/experiments/test_save.py::test_exp_save_invalid_name[invalid?name] tests/func/experiments/test_save.py::test_exp_save_invalid_name[invalidname.] tests/func/experiments/test_save.py::test_exp_save_after_commit tests/func/experiments/test_save.py::test_exp_save_with_staged_changes tests/func/experiments/test_save.py::test_exp_save_include_untracked tests/unit/repo/experiments/test_utils.py::test_resolve_exp_ref[True-True] tests/unit/repo/experiments/test_utils.py::test_resolve_exp_ref[True-False] tests/unit/repo/experiments/test_utils.py::test_resolve_exp_ref[False-True] tests/unit/repo/experiments/test_utils.py::test_resolve_exp_ref[False-False] tests/unit/repo/experiments/test_utils.py::test_run_check_ref_format[name-True] tests/unit/repo/experiments/test_utils.py::test_run_check_ref_format[group/name-False] tests/unit/repo/experiments/test_utils.py::test_run_check_ref_format[na tests/unit/repo/experiments/test_utils.py::test_run_check_ref_format[invalid/.name-False] tests/unit/repo/experiments/test_utils.py::test_run_check_ref_format[@-result4] tests/unit/repo/experiments/test_utils.py::test_run_check_ref_format[:-False] tests/unit/repo/experiments/test_utils.py::test_run_check_ref_format[^-False] tests/unit/repo/experiments/test_utils.py::test_run_check_ref_format[*-False] tests/unit/repo/experiments/test_utils.py::test_run_check_ref_format[~-False] tests/unit/repo/experiments/test_utils.py::test_run_check_ref_format[?-False]