late 15c., originally of feelings, from Middle French mutuel (14c.), from Latin mutuus "reciprocal, done in exchange," from PIE root *mei- (1) "to change, go, move," "with derivatives referring to the exchange of goods and services within a society as regulated by custom or law" [Watkins].
That is common which pertains equally to two or more persons or things. That is mutual which is freely interchanged: mutual love, affection, hatred. The word is sometimes incorrectly used for common: our mutual friend, a phrase of very frequent occurrence, no doubt owing to the perfectly correct 'mutual friendship.' [J.H.A. Günther, "English Synonyms Explained & Illustrated," Groningen, 1904]
Mutual Admiration Society (1851) seems to have been coined by Thoreau. Mutual fund is recorded from 1950. The Cold War's mutual assured destruction attested from 1966. (Assured destruction was an early 1960s term in U.S. military policy circles in reference to nuclear weapons as a deterrent, popularized c. 1964 by Robert McNamara, U.S. Secretary of Defense under Lyndon Johnson, e.g. statement before House Armed Services Committee, Feb. 18, 1965; the mutual perhaps first added by Donald Brennan, conservative defense analyst and a public critic of the policy, who also noted the acronym MAD.)