Hyman was selected by the Florida Panthers in the fifth round (No. 123) in the 2010 NHL Draft after he had 75 points (35 goals, 40 assists) with Hamilton of the Ontario Junior Hockey League. In 2010-11, he was named the Canadian Junior A Player of the Year and RBC CJHL Player of the Year after he had 102 points (42 goals, 60 assists) in 43 games.

Hyman played collegiately at the University of Michigan, where he had 89 points (35 goals, 54 assists) in 151 games. In 2014-15, his senior season, he led the Big Ten with 54 points (22 goals, 32 assists) in 37 games and was named a First Team All-America and a Hobey Baker Award finalist.

Following his career at Michigan, Hyman opted not to sign with the Panthers. Florida traded him to the Toronto Maple Leafs on June 19, 2015, and four days later, Hyman signed a two-year, entry-level contract with Toronto.

Hyman began his pro career with the Toronto of the American Hockey League in 2015-16 and had 37 points (15 goals, 22 assists) in 59 games. He was recalled by the Maple Leafs on Feb. 29, 2016, and made his NHL debut that night against the Tampa Bay Lightning. Hyman scored his first NHL goal in a 4-3 shootout loss to the Buffalo Sabres on March 7 and finished the season with six points (four goals, two assists) in 16 games.

In 2016-17, Hyman had 28 points (10 goals, 18 assists) playing in all 82 games with the Maple Leafs. On July 5, 2017, he signed a four-year contract.

Hyman set NHL career highs in goals (15), assists (25) and points (40) in 2017-18 while again playing in all 82 games. He finished second on the Maple Leafs with a plus-22 rating and had four points (one goal, three assists) in seven games in the 2018 Stanley Cup Playoffs.

In 2018-19, Hyman became a 20-goal scorer for the first time, finishing with 21 in 71 games -- a total he matched in 57 games during the 2019-20 season.

After scoring 33 points (15 goals, 18 assists) in 43 games for Toronto in 2020-21, he signed a seven-year contract with the Edmonton Oilers on July 28. Hyman became the seventh player in Oilers history to score 50 goals in a season in a 5-3 loss to the Ottawa Senators at Canadian Tire Centre on March 24, 2024. He also joined Brayden Point and Jonathan Cheechoo as players taken in the second round of later in the NHL Draft to score at least that many.

Away from the ice, Hyman writes children's books. His third, "The Magician's Secret," the story of a young boy who was enchanted by his grandfather's stories, which take him through history, was released in May 2018.