Auchmuty was born in Portadown, County Armagh, Ireland, the elder son of James Wilson Auchmuty, a Church of Ireland clergyman, and his wife Annie Todd (née Johnston). James Johnston Auchmuty graduated from Trinity College Dublin (BA, 1931; MA, 1934; Ph.D., 1935), having been elected a scholar of the university in 1929.
Auchmuty was born in Portadown, County Armagh, Ireland, the elder son of James Wilson Auchmuty, a clergyman from the Church of Ireland, and his wife Annie Todd. His father, James Johnston Auchmuty, earned academic degrees (BA, MA, Ph.D.) from Trinity College Dublin, where he was elected a scholar in 1929.