He was Professor of English Language, Literature, Mental and Moral Philosophy at the University of Adelaide from 1894–1922, Vice-Chancellor 1916–1942 and Chancellor 1942–1948.

At Edinburgh, Mitchell's thesis was supervised by Alexander Campbell Fraser, and he was assistant to Henry Calderwood.

[2] Mitchell was Professor of English Language, Literature, Mental and Moral Philosophy at the University of Adelaide from 1894–1922.

[3] Mitchell wrote about issues overlapping philosophy of mind and science, neurology, quantum theory and philosophical psychology.

[4][5] His work is the subject of a book by W. Martin Davies, The Philosophy of Sir William Mitchell, 1861–1962 : A Mind's Own Place (2003) ISBN 0-7734-6733-5.