The son of Major Alexander Black Mitchell, a High Sheriff of Gloucestershire, he was born in Henbury, Bristol and educated at Harrow School, where he represented the school cricket team.
[2] The following season he made his first-class debut for Gloucestershire against Lancashire in the 1950 County Championship.
[3] At a time when the use of amateurs as captains was coming to an end, Mitchell was offered the role of captaining Gloucestershire after Sir Derrick Bailey resigned at the end of the 1952 season, but he turned it down citing that he didn't have the time.
[4] As a result, Gloucestershire appointed Jack Crapp, the senior professional, as its captain for the 1953 and 1954 seasons.
Mitchell married Anne Denise Perpetua Gibbs on 7 October 1950.