A first-round pick by the New York Islanders (No. 28) in the 2015 NHL Draft, Beauvillier played three seasons with Shawinigan of the Quebec Major Junior Hockey League and was captain for Team Cherry in the 2015 CHL/NHL Top Prospects Game before turning pro.

Beauvillier made the Islanders roster as a 19-year-old, picked up an assist against the New York Rangers in his NHL debut on Oct. 13, 2016 and scored his first NHL goal Oct. 18, 2016, against the San Jose Sharks. He finished his rookie season with 24 points (nine goals, 15 assists) in 66 games.

He scored an NHL career-high 21 goals in 2017-18, then had 28 points (18 goals, 10 assists) the following season, helping the Islanders reach the second round of the 2019 Stanley Cup Playoffs.

Beauvillier had 39 points (18 goals, 21 assists) in 68 games when the 2019-20 season was paused March 12 due to concerns surrounding the coronavirus. His overtime goal in Game 6 of the 2021 Stanley Cup Semifinals defeated the Tampa Bay Lightning in what was the final game at Nassau Coliseum. Beauvillier signed a multiyear contract with New York on Sept. 1, 2021, and was traded to the Vancouver Canucks on Jan. 30, 2023, with forward Aatu Raty and a conditional first-round pick in the 2023 NHL Draft for center Bo Horvat. He had 28 points (11 goals, 17 assists) in 55 games before Vancouver traded him to the Chicago Blackhawks on Nov. 28 for a conditional fifth-round pick in the 2024 NHL Draft.

The following season, Beauvillier was traded to the Nashville Predators by the Chicago Blackhawks on March 7, 2024, for a fifth-round pick in the 2024 NHL Draft. He signed a one-year, $1.25 million contract with the Pittsburgh Penguins on July 1, 2024, and was then traded to the Washington Capitals on March 7, 2025.

An alternate captain for Team Quebec at the 2014 World Under-17 Hockey Challenge, Beauvillier represented Canada at several international events and helped it win the 2015 Ivan Hlinka Memorial Cup.