c. 1400, slutte, "a dirty, slovenly, careless, or untidy woman," first attested in the Coventry mystery plays. It is paired alliteratively with sloven (q.v.), which also first appears there, and both might suggest "lewd, lascivious woman" but this is uncertain.
According to OED "Of doubtful origin," but probably cognate with dialectal German Schlutt "slovenly woman," dialectal Swedish slata "idle woman, slut," and Dutch slodde "slut," slodder "a careless man," though the exact relationship of all these is obscure.
Connection also has been suggested with Old English (West Saxon) *sliet, *slyt, "sleet, slush," and comparison made to Norwegian dialectal slutr "snow mixed with rain" (see sleet).
Chaucer uses sluttish (late 14c.) in reference to the appearance of an untidy man. Slut also came to mean "a kitchen maid, a scullery drudge" (mid-15c.); in 18c. hard pieces in a bread loaf from imperfect kneading were called slut's pennies; dust left to gather on a floor was slut's wool).
The meaning "woman of low or loose character, bold hussy," if not intended in the earliest use, is attested by mid-15c., but the primary sense through 18c. was "woman who is uncleanly as regards her person or house." Johnson has it (second definition) as "A word of slight contempt to a woman" but sexual activity does not seem to figure into his examples. Playful use of the word, "young woman, wench," without implication of messiness or loose morals, is attested by 1660s:
My wife called up the people to washing by four o'clock in the morning; and our little girl Susan is a most admirable slut, and pleases us mightily, doing more service than both the others, and deserves wages better. [Pepys, diary, Feb. 21, 1664]
Compare playful use of scamp, rogue, etc., for boys. Sometimes used 19c. as a euphemism for bitch to describe a female dog.
The specific sense of "woman who enjoys sex in a degree considered shamefully excessive" is by 1966.
A group of North Sea Germanic words in sl- mean "sloppy," and also "slovenly woman" and, less often, "slovenly man." They tend to evolve toward "woman of loose morals." Compare slattern, also English dialectal slummock "a dirty, untidy, or slovenly person" (1861), variant of slammacks "slatternly woman," said to be from slam "ill-shaped, shambling fellow." Also slammakin (from 1756 as a type of loose gown; 1785 as "slovenly female," 1727 as a character name in Gay's "Beggar's Opera"), with variants slamkin, slammerkin. Also possibly related are Middle Dutch slore "a sluttish woman," Dutch slomp, German Schlampe "a slattern."