Gauthier was selected by the Toronto Maple Leafs in the first round, 21st overall, of the 2013 NHL Entry Draft after spending three years with the Rimouski Océanic in the Quebec Major Junior Hockey League (QMJHL).

During his developmental years with the Maple Leafs American Hockey League affiliate, the Toronto Marlies, he helped them clinch their first Calder Cup in franchise history.

A native of Quebec, Gauthier developed in its local minor ice hockey programs and intended to pursue a collegiate career rather than the QMJHL.

After his selection by the Océanic in the QMJHL and Youngstown Phantoms in the United States Hockey League, he was encouraged by Sidney Crosby to pursue a career in his native province.

[4] Gauthier eventually advanced to the Collège Esther-Blondin Phénix in midget AAA[5] and led the team to the 2012 Telus Cup.

[6] He competed in the CHL Top Prospects Game[10] and received a final ranking of eighth amongst North American skaters from the NHL Central Scouting Bureau.

[22] After attending the Maple Leafs' training camp, Gauthier joined the American Hockey League Toronto Marlies for the 2015–16 season.

During those seven games, Gauthier recorded his first career NHL point on April 6, 2016, with an assist on Morgan Rielly's second period goal.

While playing in the second-round against the Syracuse Crunch, Gauthier suffered an avulsion of the hamstring injury which required surgery, ending his season.

[32] Gauthier was invited to participate in the Toronto Maple Leafs training camp prior to the 2017–18 season,[33] although he was reassigned to the Marlies.

"[45] After sitting as a healthy scratch for four consecutive nights, Gauthier returned to the Leafs lineup to reach a new career-high in goals.

[48] As a free agent over the summer and approaching the 2021–22 season, Gauthier for the second consecutive year signed a Professional Tryout contract in accepting an invitation to attend the New Jersey Devils training camp on September 18, 2021.

[50] After two seasons in Switzerland with Ajoie, Gauthier left as a free agent and opted to sign a one-year deal with Russian club, Vityaz Moscow Region of the KHL, on May 29, 2024.

[59] He played on a line with Lawson Crouse and Nick Ritchie during the tournament,[60] as Team Canada won a gold medal.