He was born in Streatham, London, educated at Epsom College, Surrey and Goldsmiths College, University of London and worked as an engineer at the Midland Railway Works at Derby before studying engraving at Goldsmiths College from 1921 to 1926. In 1927 he married Kathleen Barry.
His early prints of pastoral subjects show the influence of Samuel Palmer. He did not begin to paint in earnest until he was in his mid-30s, following the collapse of the print market in 1930 due to the Great Depression. These pieces are mainly landscapes, which show an affinity with the work of Paul Nash. Sutherland focused on the inherent strangeness of natural forms, and abstracting them, sometimes giving his work a surrealist appearance; in 1936 he exhibited in the International Surrealist Exhibition in London.
He also took up glass design, fabric design and poster design during the 1930s, and taught at a number of London art colleges. In 1934 he first visited Pembrokeshire, and the place remained an inspiration for his neo-romantic work until late 1936.
From 1940 he was employed as an official artist in World War II, as part of the War Artists' Scheme. He worked on the Home Front, depicting mining, industry, and bomb damage.
Having converted to Catholicism in 1926, from around 1950 until his death he was deeply involved in religion. Following the war he produced several religious pieces, including The Crucifixion (1946) for St. Matthew's Church, Northampton and the tapestry Christ in Glory (1962) for Coventry Cathedral. He also continued to produce work based on natural forms, and managed to blend some of these - such as thorns - into his religious work. Sometimes, as in Head III (1953), these forms, often considered threatening in appearance, have an organic appearance but are entirely invented.
From 1947 into the 1960s his work was inspired by the south of France, and he purchased a villa there at Menton in 1955.
Sutherland also painted a number of portraits, with one of Somerset Maugham (1949) the first and among the most famous. His painting of Winston Churchill (1954) was famously destroyed on the orders of Lady Churchill; studies for the portrait have survived, however.
The main Art & Design building at Coventry University is named after him.
There were major retrospective shows at the Tate Gallery in 1982, France in 1998, and the Dulwich Picture Gallery in 2005.