"a person, an individual," c. 1300, from piece (n.1), but in modern use contemptuous and commonly of women; the meaning "person regarded as a sex object" is by 1785. Compare piece of ass under ass (n.2); human beings colloquially have been piece of flesh from 1590s; also compare Latin scortum "bimbo, anyone available for a price," literally "skin."
PIECE. A wench. A damned good or bad piece; a girl who is more or less active and skilful in the amorous congress. Hence the (Cambridge) toast, may we never have a PIECE (peace) that will injure the constitution. [Dictionary of Buckish Slang, University Wit and Pickpocket Eloquence, London, 1811]
familiar term for an ass, 1785, also donky, donkie, originally slang or dialectal, of uncertain origin. Perhaps a diminutive from dun "dull gray-brown" (from Middle English donned, past participle of donnen "to lose color, fade, from Old English dunnian). Compare Dunning, name of a (dun) horse (mid-14c.), and see dun (adj.). The form perhaps was influenced by monkey.
Or perhaps it is from a familiar form of the proper name Duncan applied to an animal (compare dobbin). The older English word was ass (n.1). Applied to stupid, obstinate, or wrong-headed persons by 1840. In mechanics, used of small or supplementary apparatus from mid-19c. (donkey-engine, donkey-pump, etc.). Short form donk is by 1916.
mule born of a horse and a she-ass, late 14c., from Latin burdonem.
"a mule got from a she-ass by a stallion," 1680s, from Latin hinnus, from Greek innos, ginnos, of unknown origin.
by 1997, online abbreviation of laughing my ass off. Related: LMFAO (by 2000).
American English initialism (acronym) for district attorney from 1934; for duck's ass haircut (or, as OED would have it, duck's arse), from 1951. The haircut so called for the shape at the back of the head.
"not acting right," 1969, African-American vernacular, from jive (n.). Extended form jive-ass (1964, adj.; 1969, n.) is defined in OED as "A word of fluid meaning and application," but generally disparaging.