Born in Wealdstone, Middlesex, he was brought up in Swansea and went to evening classes at Swansea College of Art in 1930. He moved to Barnoon, St Ives to help an aunt renovate a cottage in 1930, and opened a market garden in 1938.  At Geevor Mine he also worked as a tin miner between 1942 and 1945, then a fisherman from 1946 to 1948.

His interest in modern art was aroused by meeting Bernard LEACH and Adrian STOKES when they were in the Home Guard during the War. With his brother Endell he organised the first show of modern art in St Ives at the Castle Inn. Initially he tried his hand as a painter of land and seascapes. But, when he became assistant to Barbara HEPWORTH in 1949, he first started to sculpt in wood and eventually turned to bronze, the work for which he became best known. He was assistant to Hepworth from 1949 to 1959. He began to sculpt in bronze in 1959.

Mitchell was a much loved and respected friend to many artists. For a great many years he shared a studio with the painter John WELLS.