McMahon graduated from the University of Glasgow with a Bachelor of Science degree in 1981. Four years later he was given a Doctor of Philosophy degree from the King's College in London.
McMahon began his career as a post-doctoral fellow at J. Michael Bishop’s laboratory in the Hooper Foundation of the University of California in San Francisco (UCSF) in 1981, in order to study oncogenic protein kinases. In 1991, he established an independent research group at the DNAX Research Institute (nowadays Merck Research Labs) working on RAF protein kinases. From 1991 to 1998, McMahon pioneered the use of a new class of conditional oncoproteins to dissect the corrupting events that lead normal cells to develop aberrant properties of lethal cancer.
Then in 1998, Martin was recruited to the faculty of the UCSF Cancer Research Institute of Helen Diller Family Comprehensive Cancer Center, where he served as the Efim Guzik Distinguished Professor of Cancer Biology, Co-Leader of the Experimental Therapeutics Program and Director for Professional Education.
In 2015, he joined the faculty of the Department of Dermatology and the Huntsman Cancer Institute of the University of Utah as the Cumming-Presidential Professor of Cancer Biology and the Senior Director for Preclinical Translation.
McMahon is the president of the Society for Melanoma Research. He has served on the editorial board of Molecular Cancer Research, Molecular and Cellular Biology and Pigment Cell & Melanoma Research.
On May 25, 1995 Martin McMahon married Karen Michele Devaney.