late 15c., "reciprocally given and received," originally of feelings, from Old 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].
The meaning "common" is from 1630s. "Used in this sense loosely and improperly (but not infrequently, and by many writers of high rank), especially in the phrase a mutual friend" [Century Dictionary].
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 is attested from 1966. Assured destruction was a 1962 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 notion was "the minimum threat necessary to assure deterrence: the capability to exterminate not less than one third of the Union of Soviet Socialist Republics' (USSR) population in a retaliatory nuclear attack." [Martin Folly, "Historical Dictionary of U.S. Diplomacy During the Cold War"].
By 1964, as the Soviet Union caught up to NATO in ICBMs, the mutual was added, perhaps first by Donald Brennan, conservative defense analyst and a public critic of the policy, who also noted the acronym MAD.)