Mitchell was born at Creswell, Bolsover, Derbyshire and was a faceworker in the coal mines. He was first spotted by Derbyshire during the General Strike of 1926 and began playing for Derbyshire in the 1928 season but was disappointing. However in the 1929 season he took 100 wickets and was deadly whenever the pitches took sufficient spin. In the 1930 season, he did even better, and though expensive in the 1931 and 1932 seasons, his ability to spin the ball on dry pitches more than any other leg-spinner in county cricket saw him taken on the Ashes tour (in preference to the likes of Tich Freeman) when Business prevented Walter Robins touring. He played in the Fourth Test as a replacement for Bill Voce who was injured, and despite dismissing Bill Woodfull in both innings he was never able to establish himself for England. Indeed, he was so expensive when called upon in 1934 that he took no wicket and conceded 117 runs, and the following year, when he was very disappointing on a leatherjacket-infested Lord's wicket that should have helped him, he is quoted as having said "You couldn't captain a team of bloody lead soldiers" to his captain Bob Wyatt. Indeed, Mitchell's tactlessness towards administrators made him quite unpopular with them and may have prejudiced his chances of doing well in representative cricket.
A leg spin Bowler, he was the most successful slow Bowler in the history of a county better known for its pace bowling strength. His bowling was an important factor in Derbyshire's most successful period in the County Championship during the 1930s. Along with Bill Copson, Leslie Townsend and the brothers Pope, he formed an attack sufficiently strong during the dreadful summer of 1936 to, aided by some quirks in the weather, displace Yorkshire from their perennial position atop the Championship table.
However, for Derbyshire Mitchell went from strength to strength in the dry summers of 1933 and 1934, at times bowling with sensational skill, as when he dismissed Worcestershire for 48 on a good pitch in 1934. He was close to the top of the averages in those two seasons, but from the 1935 season appeared to sacrifice length to gain more spin and often suffered heavy punishment. Still, he could be deadly on his best days, as when he took all ten wickets in an innings against Leicestershire for 64 runs at Leicester in 1935 or when he took 7 for 26 against Gloucestershire on a blameless pitch at Derby a year later. Mitchell set a record for Derbyshire with 168 wickets in 1935, but in Derbyshire's Championship win in the 1936 season he was considerably less successful and at times very expensive even when conditions favoured bowlers (e.g. against Kent at Burton-on-Trent and Warwickshire at Edgbaston). Still, on Mitchell's good days Derbyshire's bowling that season could compare with almost any county side in history, and the following two seasons still saw him as one of the best spin bowlers in England.
In the 1939 season, however, Mitchell did not do much work because Derbyshire's pace attack was so consistently effective and he failed to take 100 wickets for the first time in 11 seasons. Moreover, when he refused to rejoin the team after World War II, the Derbyshire committee declined to give Mitchell the benefit he had been due to receive in 1940. He did, though, continue to baffle batsmen for Hickleton Main well into his fifties.