Mangiapane made an immediate impact as a rookie for Barrie of the Ontario Hockey League in 2013-14 when he was named to the OHL First All-Rookie Team after he had 51 points (24 goals, 27 assists). It got better the next season with 104 points (43 goals, 61 assists) and 106 points (51 goals, 55 assists) as Colts alternate captain in 2015-16 after he was selected by the Calgary Flames in the sixth round (No. 166) of the 2015 NHL Draft.
Mangiapane signed an entry-level contract with the Flames on March 23, 2016 and played the next two seasons for Stockton of the American Hockey League. He played 44 NHL games in 2018-19 and emerged as a regular in 2019-20.