After turning professional, Wirral-born Mountfield spent a season-and-a-half at local club Tranmere Rovers before moving across the River Mersey to play for Everton.
He formed a defensive partnership with Kevin Ratcliffe and helped the club to victory in the 1984 FA Cup Final against Watford and to the Football League title the following season.
In 1989–90, it looked as though Mountfield would add another league title medal to the two he won with Everton, as Villa topped the First Division on several occasions, but eventually they finished second behind champions Liverpool.
His final club as a player was Scarborough, and he played six Division Three games for them late in the 1998–99 season, but was unable to prevent their relegation from the Football League.
In 2000, League of Ireland team Cork City appointed former Shelbourne boss Colin Murphy as successor to Dave Barry.
After relative success in preceding seasons crowds again dwindled as the team struggled and the increasingly unpopular Mountfield was sacked in January, after just six months in charge and a 4–0 defeat at home to St Patrick's Athletic.