Clearance of entangled DNA from the anaphase mid-region must accurately proceed in order for chromosomes to segregate with high fidelity. Loss of Taz1 (fission yeast ortholog of human TRF1/TRF2) leads to stalled telomeric replication forks that trigger telomeric entanglements; the resolution of these entanglements fails at ≤20°C. Here, we investigate these entanglements and their promotion by the conserved replication/repair protein Rif1. Rif1 plays no role in taz1Δ fork stalling. Rather, Rif1 localizes to the anaphase mid-region and regulates the resolution of persisting DNA structures. This anaphase role for Rif1 is genetically separate from the role of Rif1 in S/G2, though both roles require binding to PP1 phosphatase, implying spatially and temporally distinct Rif1-regulated phosphatase substrates. Rif1 thus acts as a double-edged sword. Although it inhibits the resolution of taz1Δ telomere entanglements, it promotes the resolution of non-telomeric ultrafine anaphase bridges at ≤20°C. We suggest a unifying model for Rif1's seemingly diverse roles in chromosome segregation in eukaryotes.