Dumont was selected by the Montreal Canadiens in the fifth round (No. 139) of the 2009 NHL Draft after he had 49 points (28 goals, 21 assists) in 51 games for Drummondville of the Quebec Major Junior Hockey League.

He followed that up with 93 points (51 goals, 42 assists) in 62 games the following season and signed a three-year, entry-level contract with the Montreal Canadiens on April 30, 2010.

Dumont spent most of the next two seasons with Hamilton of the American Hockey League before making his NHL debut on April 4, 2012 against the Tampa Bay Lightning and scored his first career goal in a 6-4 loss to the Pittsburgh Penguins on April 17, 2013.

Dumont signed a two-year, two-way contract with the Canadiens on July 10, 2013, but after playing for St. John's of the AHL in 2015-16, he signed a one-year, two-way contract with the Lightning on July 1, 2016. That season, he had four points (two goals, two assists) in 39 games for Tampa Bay.

In 2017-18, Dumont appeared in seven games (no points) with the Lightning before he was placed on waivers on Nov. 21, 2017. He was claimed by the Ottawa Senators the next day and had two points (one goal, one assist) in 23 games with Ottawa before being waived on Feb. 20, 2018. He was claimed by the Lightning the next day and assigned to Syracuse of the AHL, where he had 21 points (five goals, 16 assists) in 18 games.