Leipsic played in the WHL from the 2010–11 season. He was a member of Canada's National Junior Team for the 2012 Canada-Russia Challenge. In the 2012–13 season with the Portland Winterhawks, Leipsic scored 120 points in 68 games to win the CHL Top Scorer Award as the highest-scoring player in the Canadian Hockey League. Leipsic was selected by the Nashville Predators in the third-round of the 2012 NHL Entry Draft. On May 23, 2013, the Predators signed Leipsic to a three-year entry-level contract. Leipsic was assigned to the Predators AHL affiliate, the Milwaukee Admirals to begin his first professional season in 2014–15. He led the Admirals in rookie scoring with 36 points in 47 games. On February 15, 2015, the Predators traded Leipsic along with Olli Jokinen and Nashville's 2015 first round draft pick to the Toronto Maple Leafs in a package deal for Cody Franson and Mike Santorelli. Leipsic played an important role down the stretch in helping the Toronto Marlies reach the post-season. Leipsic began the 2015–16 season with the Marlies, and would play there for most of the year. However, in February 2016, the Maple Leafs lineup was depleted due to injuries. Wanting to allow younger players to remain in the AHL and develop, Toronto initially called up older veterans. When injury struck again however, Leipsic was called up on February 13, 2016, in reward for his strong play, along with Jeremy Morin, both on an emergency basis. Leipsic made his debut the same night, in a road game against the Vancouver Canucks, and scored his first NHL goal midway through the second period, batting a flying puck out of mid-air and past goaltender Ryan Miller. The reaction of Leipsic's parents, who were in attendance and flew last minute to the game, garnered much media attention. Leipsic became the first Maple Leafs' player to score a goal in his NHL debut since Nikolay Kulemin in 2008. Leipsic was sent back to the Marlies shortly after his debut. On June 21, 2017, Leipsic was left exposed at the 2017 NHL Expansion Draft by the Toronto Maple Leafs, and was selected by the Vegas Golden Knights. He signed a two-year $1.3 million contract in July 2017. On February 26, 2018, Leipsic was traded to the Vancouver Canucks in exchange for Philip Holm. In the 2018–19 season, on December 3, 2018, Leipsic was placed on waivers by the Canucks and claimed by the Los Angeles Kings. Added to inject some spark to the cellar dwelling Kings, Leipsic displayed hustle and an ability to pick pucks off the end boards, totalling five goals, 18 points in 45 games for the Kings. With the Kings looking to turn over the roster and as an impending restricted free agent, Leipsic was not tendered a qualifying offer by the Kings and was released as a free agent on June 25, 2019. He was signed by the Washington Capitals to a one-year, $700,000 contract on July 1, 2019.
Leipsic, along with fellow player Jack Rodewald, were the subject of controversy after a conversation on Leipsic's Instagram account was leaked to the public. Leipsic and Rodewald were caught making misogynistic and derogatory remarks about the girlfriend of Connor McDavid and the wife of Tanner Pearson. Leipsic also took shots at former teammate Jake Virtanen and his then-current Capitals teammates Garnet Hathaway and Nic Dowd. On May 6, 2020, Leipsic apologized for his conduct and deleted his Instagram account. On May 8, 2020, the Capitals placed Leipsic on unconditional waivers for purposes of terminating his contract. Leipsic cleared waivers the following day and his contract was terminated.
