Cumming was born in Dunfermline, Fife. He was educated at Dunfermline High School where he displayed an early determination to become an artist, winning an Andrew Grant Scholarship to attend the Edinburgh College of Art between 1939 and 1947. His studies were interrupted by the War and in 1941 he joined the Royal Air Force, completed pilot training at Terrell, Texas, in 1944 and served in RAF Transport Command in India and Burma.
Returning to his studies at Edinburgh College of Art, he completed his Diploma in 1948 and his postgraduate degree a year later. He was awarded a Travelling Scholarship, which he used to live and work in the remote island community of Callanish on the Isle of Lewis. He created a series of paintings, known as the Hebridean paintings, during this period that later helped to establish him as painter of The Edinburgh School.
From 1950 he lectured at Edinburgh until his retirement in 1982, teaching both in the Humanities and the Painting school. Students of Cumming included Sandy Moffat, John Bellany and latterly Richard Wright who won the Turner Prize in 2009. Cumming is remembered with great affection for his gentlemanly encouragement, sparkling wit and the range of his intellect. He was elected Academician of the Royal Scottish Academy in 1970 and acted as its Secretary between 1978 and 1980. His daughter Laura Cumming was art critic of The Observer newspaper.
A retrospective was held at the Talbot Rice Gallery in Edinburgh.