Mellis was born in China to Scottish parents and moved to Britain when she was one year old. She studied at Edinburgh College of Art under S. J. Peploe, winning a scholarship to study in Paris in 1933. In 1939 Mellis moved to St Ives with her husband, the writer Adrian Stokes. There, she became part of the St Ives group of artists and produced constructions of plywood, driftwood and found objects in addition to painting. In the 1960s and 1970s she experimented with constructions and reliefs in colour. Since 1978 she made reliefs using driftwood.