Born in Aberdeen, Mutch started his football career with Avondale before joining Banks O' Dee.
After leaving, he went to Preston North End, where he helped the club win the 1938 FA Cup final, the first to be shown on television.
He scored the resulting penalty kick, which rebounded from the underside of the bar, to win the match for Preston North End.
After a season with Bury, he joined Southport as a player-trainer, before taking up his training responsibilities on a permanent basis in 1948.
He earned one cap for the Scotland national football team, a 1–0 win over England at Wembley Stadium on 9 April 1938.