During the 2014–15 season, Hyman won a number of awards, including being named the University of Michigan's Athlete of the Year and a First Team All-American, and was a finalist for the Hobey Baker Award.
Hyman was selected by the Florida Panthers in the fifth round of the 2010 NHL entry draft. However, the parties were unable to agree on a contract, and Hyman's rights were traded to the Toronto Maple Leafs on June 19, 2015. During his rookie 2016–17 season, he set a new Maple Leafs record for most short-handed goals scored by a rookie in a season with four, and tied the team record for the most consecutive games with an assist by a rookie at six games.
Hyman has been nicknamed "Shaq Hyman" by fans, staff, and media alike due to his "in the crease" style of play. O'Neal himself has acknowledged and approved of the nickname. Hyman gifted Shaq a custom signed jersey and stick, much to O'Neal's delight. O'Neal returned the gesture by sending Hyman a signed Lakers jersey.