"flesh of sheep used as food," c. 1300, mouton (c. 1200 as a surname), from Old French moton "mutton; ram, wether, sheep" (12c., Modern French mouton), from Medieval Latin multonem (8c.), probably [OED] from Gallo-Roman *multo-s, accusative of Celtic *multo "sheep" (source also of Old Irish molt "wether," Mid-Breton mout, Welsh mollt), which is perhaps from PIE root *mel- (1) "soft."
The same word also was borrowed into Italian as montone "a sheep," and mutton in Middle English also could mean "a sheep" (early 14c.). Transferred slang sense of "food for lust, loose women, prostitutes" (1510s) led to extensive British slang uses down to the present day for woman variously regarded as seeking lovers or as lust objects. Mutton chop "cut of mutton (usually containing a rib) for cooking" is from 1720; as a style of side whiskers from 1865, so called for the shape (narrow and prolonged at one end and rounded at the other).
verb ("to ejaculate") and noun ("semen"), by 1973, apparently a variant of come in the sexual sense that originated in pornographic writing, perhaps first in the noun. This "experience sexual orgasm" slang meaning of come (perhaps originally come off) is attested by 1650, in "Walking In A Meadowe Greene," in a folio of "loose songs" collected by Bishop Percy.
They lay soe close together,
they made me much to wonder;
I knew not which was wether,
vntill I saw her vnder.
then off he came & blusht for shame
soe soone that he had endit;
yet still shee lyes, & to him cryes,
"Once More, & none can mend it."
It probably is older and disguised in puns, e.g. "I come, I come, sweet death, rock me a-sleep!" ["Nashe His Dildo," 1590s]
As a noun meaning "semen or other product of orgasm" come is attested by the 1920s.
The sexual cum seems to have no connection with Latin cum, the preposition meaning "with, together with, in connection with" (an archaic form of com; see com-) which English uses on occasion in names of combined parishes or benefices (such as Chorlton-cum-Hardy), in popular Latin phrases (such as cum laude), or as a combining word to indicate a dual nature or function (such as slumber party-cum-bloodbath).