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). Gauthier became a member of the Toronto Maple Leafs organization following the 2014–15 season. 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.