slang, "perform male masturbation," by 1896, from jerk (v.) denoting rapid pulling motion + off (adv.). Compare come off "experience orgasm" (17c.). Farmer and Henley ("Slang and Its Analogues") also lists as synonyms jerk (one's) jelly and jerk (one's) juice. The noun jerk off or jerkoff as an emphatic form of jerk (n.2) is attested by 1968. As an adjective from 1957.
by 1942, noun ("a cowardly escape, an evasion") and verb ("sneak off, escape, give up without trying"), American English slang, perhaps from cop a plea (c. 1925) "plead guilty to lesser charges," which is probably from northern British slang cop "to catch" (a scolding, etc.); as in cop a feel "grope someone" (1930s); see cop (v.). Sense of "evade an issue or problem" is from 1960s.