George Archibald Grant Mitchell was born on 11 November 1906 and was educated at Aberdeen University, where he graduated in medicine. He lectured at Aberdeen until the outbreak of the Second World War, working under Professor J R Learmonth.
During the War Mitchell served with the Middle East Force, initially attached to the 15th (Scottish) General Hospital, in charge of orthopaedic centre no.1 in Cairo. He was later officer-in-charge of the surgical division of 42 General Hospital, Middle Eastern Forces. Mitchell was then appointed to undertake field trials with penicillin with the 8th Army during its campaigns in Libya and Italy. In February 1944, Mitchell was appointed adviser in penicillin and chemotherapy for 21 Army Group. The 21 Army Group was a British headquarters formation commanded by Bernard Montgomery, which played an important role in the European campaigns in 1944-5. During his period in the North African theatre, Mitchell developed new antibiotic treatments for wound therapy, and in 1944 he undertook the planning of antibiotic therapies in anticipation of the casualties expected during the invasion of western Europe. Mitchell encouraged the prophylactic use of penicillin, and introduced intramuscular drips to ensure that the drug could be administered continuously. He was appointed OBE for this work in 1945.
In 1946 Mitchell was appointed as professor of anatomy at the University of Manchester, and served in this post until 1974. He was dean of the medical school from 1955 to 1960 and a pro-vice chancellor of the University between 1959 and 1963. At Manchester, Mitchell was known for his work on neuroanatomy and the renal nerves. During the 1950s and 1960s, Professor Mitchell was an active member of the International Anatomical Nomenclature Committee, which devised an agreed medical terminology for anatomy, histology and embryology. Mitchell was president of the Manchester Medical Society and president of the Anatomical Society of Great Britain. He was president of the Third European Anatomical Congress in 1973. He was a member of the board of governors of the United Manchester Hospitals from 1955 to 1974. Mitchell died on 14 April 1993.
Professor Mitchell married Mary Cumming in 1933, who predeceased him. They had three children.