Mitchinson was the son of the Labour politician Dick Mitchison and his wife, the writer Naomi (née Haldane). The biologist J.B.S. Haldane was his uncle, and the physiologist John Scott Haldane was his maternal grandfather. His elder brother is the bacteriologist Denis Mitchison, and his younger brother is the zoologist Avrion Mitchison. His wife was the historian Rosalind Mitchison.
Mitchison went to Winchester College and Trinity College in Cambridge, and later became Professor of Zoology at Edinburgh University in 1963 after working there for a decade. He was elected a fellow of the Royal Society of London in 1978.
Considered a pioneer in the area of cellular biology, Mitchison developed the yeast Schizosaccharomyces pombe as a model system to study the mechanisms and kinetics of growth and the cell cycle. He was an academic advisor to the 2001 Nobel Prize in Physiology recipient Paul Nurse.
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