He was the son of Patrick Cumin (died 27 October 1820), professor of oriental languages at the University of Glasgow, and his wife Rachael Baird. The Scottish philosopher David Hume in a letter to Adam Smith in June 1761 had recommended Cumin's father for his position.
Cumin left the University of Glasgow in 1840 to take up residence at Clifton, Bristol. He married Ann Johnstone Ker at Glasgow and at Edinburgh in 1821. Cumin died at Bath in 1854. His grandson, Henry Patrick Cholmeley, MB from the University of Oxford in 1886, was the author of John of Gaddes and the Rosa Medicinae (1912).
Cumin's niece, Robina Anne Wilson (30 November 1813 – 28 July 1855), the wife of Leopold Cattani Cavalcanti, is buried at the celebrated Protestant Cemetery at Florence with, among other members of the expatriate British community, the poet Elizabeth Barrett Browning.
- Bryce, J. C. and Skinner, A. S. (editors) (1976) The Glasgow Edition of the Works and Correspondence of Adam Smith, Oxford, Oxford University Press.
- Comrie, John D. (1927) History of Scottish Medicine to 1860, London, Ballière, Tindall & Cox.