Axelrod was born in New York City and educated there at the City College. Unable to finance a medical career, Axelrod worked from 1935 to 1945 as a technician in a laboratory of industrial hygiene that had just been set up in New York. But still with an ambition for a career in scientific research, and after some years at the Goldwater Memorial Hospital and the National Heart Institute, he took a year off in 1955, obtained a PhD from George Washington University, and moved to the National Institute of Mental Health as chief of the pharmacology section. He held this post until his retirement in 1984, while also continuing to work in the cell biology laboratory at the NIMH.

Axelrod has thrown much light on the action of the catecholamines, the neurotransmitters of the sympathetic nervous system. The most important of these is norepinephrine, first identified as a neurotransmitter by Ulf von Euler in 1946. Axelrod realized that once the molecule had interacted with its target cell some mechanism must come into action to switch it off. Later he was able to describe the role of two enzymes, catechol-o-methyltransferase (COMT) and monoamine oxidase (MAO), which degrade the catecholamines.

However, studies with radioactive norepinephrine showed its persistence in the sympathetic nerves for some hours. This led Axelrod to propose that norepinephrine is taken up into, as well as released from, sympathetic nerves. This recapture inactivates the neurotransmitter.

For work on the catecholamines Axelrod shared the 1970 Nobel Prize for physiology or medicine with von Euler and Bernard Katz.

Axelrod has also worked on the role of the pineal gland in the control of circadian rhythms, and the neuropharmacology of schizophrenia.