Davie was born in Grangemouth in 1920 and studied at Edinburgh College of Art in the late 1930s. An early exhibition of his work came through the Society of Scottish Artists.
After the Second World War, Davie travelled widely and in Venice became influenced by other painters of the period, such as Paul Klee, Jackson Pollock and Joan Miró, as well as by a wide range of cultural symbols. In particular, his painting style owes much to his affinity with Zen. Having read Eugen Herrigel's book Zen in the Art of Archery (1953) he assimilated the spontaneity which Zen emphasises.
Declaring that the spiritual path is incompatible with planning ahead, he has attempted to paint as automatically as possible, which is intended to bring forth elements of his unconscious. In this, he shares a vision with surrealist painters such as Miró, and he has also been fascinated by the work of psychoanalyst Carl Jung.
Like Pollock, many of Davie's works have been executed by standing above the painting, which is laid on the ground. He added layers of paint until sometimes the original painting has been covered over many times. Despite the speed at which he worked (he usually had several paintings on the go at once), however, he was adamant that his images are not pure abstraction, but all have significance as symbols. Championing the primitive, he saw the role of the artist as akin to that of the shaman, and remarked upon how disparate cultures have adopted common symbols in their visual languages.