Muriel Florence Snell Shaw (nee Foote) was born in Ipswich in 1911. During her time, from 1925 to 1928, at the Presbyterian Girls College in Warwick she acquired the lifelong nickname 'Mim'. She matriculated at University of Queensland in 1929, having studied Latin, math, geology, and psychology. From 1930 to 1934 she attended Vida Lahey's painting and drawing classes in Brisbane. During this time she also studied pottery with L. J. Harvey (Lewis Jarvis Harvey (1871-1949)). Mim moved to Sydney in 1935 at the suggestion of Vida Lahey. From 1935 to 1938 she attended Adelaide Perry's School for Painting and Drawing. Macquaries Galleries held an exhibition called 'A Group of Young Painters' in 1937 in which she participated.

In 1938 she sailed to London where she enrolled at Westminister Art School. During this time, she also made sketching trips to Europe.

With the outbreak of World War II, Muriel returned to Brisbane. While in Brisbane in 1941, she taught lunch-time lectures on Friday's at the Art Reference Library which was established by Daphne Mayo and Vida Lahey in 1936. From 1941 to 1945 she taught weaving, pottery, painting and art history at St Hilda's Grils School in Stanthorpe and Moreton Bay High School, and assisted with Vida Lahey's afternoon painting and drawings classes for children.

In 1945 Mim married bio-chemist James Graham Shaw and they moved to Sydney in 1946. They had two daughters Helen Jane and Margaret Evelyn.

From 1954 to 1955 she attended Dora Sweetapple's art school in Woollahra. Mim resumed teaching art and geography in 1957. When her husband, James Shaw, died in 1958, she was able to support her young family with her teaching. Upon returned to Brisbane in 1971, she joined the Half Dozen Group of Artists which was located at St Mary's Anglican Church, Kangaroo Point. She became the group's secretary in 1972 and Vice-President in 1974. She was also a member of the Royal Queensland Art Society.

Mim studied Fine Arts at the University of Queensland from 1979 to 1982. After the death of Daphne Mayo in 1982, Mim was one of the organisers of the 'Friends of Daphne Mayo' group, and her address was used in correspondence for the group. This group was the publisher of Judith McKay’s memorial booklet 'Daphne Mayo : a tribute to her work for art in Queensland', published in 1983. Mim wrote and/or drafted correspondence regarding the booklet, promoting it and sending it to people and libraries as required. Mim also wrote an account of Vida Lahey, as suggested to her by Daphne Mayo.

Mim died of bowel cancer on 11 June 1990. Mim was more widely known as a painter and print-maker but she also studied pottery, screen-printing, design, batik, and weaving.