 Axelrod was drafted in the 30th round, 927th overall, of the 2007 MLB Draft by the San Diego Padres.Axelrod debuted in 2007 with the Arizona League Padres of the Rookie Arizona League, going 0–2 with 2 saves in 11 games exclusively as a reliever with a 5.40 ERA, before earning a promotion to the Fort Wayne Wizards of the A Midwest League, where in 10 games out of the pen he had a 1.27 ERA.He started 2008 with the Lake Elsinore Storm of the A+ California League, going 2–1 as a reliever in 32 games with a 5.29 ERA, before being sent back to Fort Wayne, where he finished the year going 1-1 with a 3.95 ERA.