Raised in Port Dover, Ontario, Axford attended Assumption College School in nearby Brantford. Because the school didn't have an interscholastic baseball program, he played for Port Dover Minor Baseball, Team Ontario and Team Canada. His combined four-year totals with the three clubs were a 37–12 record, a 1.88 earned run average (ERA), 278 innings pitched, 432 strikeouts and 173 walks.

He was originally selected by the Seattle Mariners in the seventh round (219th overall) of the 2001 Major League Baseball (MLB) draft, but accepted an athletic scholarship to the University of Notre Dame instead. He was inactive during his junior year after undergoing Tommy John surgery in December 2003. Used as a starting pitcher in 26 of 36 games, his record in three seasons with the Fighting Irish was 14–6. Despite losing his scholarship as a redshirt senior in 2005, he still earned a bachelor's degree in film, television and theatre.