Clifford was born at Napperby Station, North West of Alice Springs to Tjatjiti Tjungurrayai and Long Rose Nangala. He lived a very traditional bush upbringing in his youth in the Jay Creek area and later became a stockman. He is from a family of artists, both his stepfather and brother having artwork displayed on Australian postage stamps. Another older brother, Cassidy, was also a painter and a respected elder in his community.

Clifford began his art career with wood carving and would carve snakes and goannas.When acrylic painting came to the Papunya area in the early 1970's, Clifford Possum emerged as one of the first artists to be involved in the Western Desert Art Movement.

Clifford passed away in June 2002 not long after being officially recognised for all his work and contribution to the Aboriginal Art and Culture in Australia. He was to be sworn in as an officer of the Order of Australia.