His father, Ted, was also a New Zealand international, while his grandfather, William Mincham played for Auckland and later became a senior club, and international referee.
In 1967 Mincham won the Tetley Trophy as the leading try scorer in the Auckland Rugby League competition when he scored 19 tries that season.[3] He was not selected for the Kiwis in 1967 but in 1968 was named as part of the 1968 World Cup squad. Mincham played in three matches at the tournament.[4]