Leivo was selected by the Toronto Maple Leafs in the third round (No. 86) in the 2011 NHL Draft after he had 30 points (13 goals, 17 assists) in 64 games with Sudbury of the Ontario Hockey League.

In 2011-12, he had 73 points (32 goals, 41 assists) in 66 games with Sudbury before appearing in one game for Toronto of the American Hockey League. The following season, he had a combined 73 points (29 goals, 44 assists) in 63 games with Sudbury and Kitchener of the OHL and appeared in four more games for Toronto of the AHL, getting two assists.

On March 5, 2013, the Maple Leafs signed Leivo to a three-year, entry-level contract.

Leivo made his NHL debut on Oct. 10, 2013, against the Nashville Predators and scored his first goal in a 3-2 loss to the Carolina Hurricanes one week later. He had two points (one goal, one assist) in seven games before he was sent down to the AHL on Oct. 26. He had 42 points (23 goals, 19 assists) in 59 games.

Leivo spent most of the 2014-15 season with Toronto of the AHL, where he had 32 points (11 goals, 21 assists) in 51 games. He played in nine games with the Maple Leafs, scoring one goal.

Named to the 2016 AHL All-Star Classic on Jan. 6, 2016, Leivo finished the season with 48 points (17 goals, 31 assists) in 51 games and led Toronto forwards with 12 points (four goals, eight assists) in 15 games in the Calder Cup Playoffs. He also played in 12 games with the Maple Leafs and had five points, all goals.

On July 21, 2016, Leivo signed a two-year contract with the Maple Leafs. He appeared in 29 NHL games during the next two seasons and had 14 points (three goals, 11 assists).