He is a former Professor of Philosophy and Pro-Vice-Chancellor, now Professor Emeritus, of Cambridge University. After studying chemical engineering at university, he took up philosophy. His primary work is metaphysics, although his philosophical interests include philosophy of science, philosophy of mind, probability, time and causation, laws of nature and properties, and decision theory.
Mellor was Professor of Philosophy at the University of Cambridge and Fellow of Darwin College from 1971 to 2005.
He was a Fellow of the British Academy between 1983 and 2008. In retirement Mellor now holds the title of Emeritus Professor.
Mellor is also an amateur theatre actor.
He was president of the Aristotelian Society from 1992 to 1993, a member of the Humanist Philosophers" Group of the British Humanist Association and Honorary Fellow of the Australian Academy of the Humanities.