cast-off adj.

c. 1200, "throw, throw violently, fling, hurl," from a Scandinavian source akin to Old Norse kasta "to throw" (cognate with Swedish kasta, Danish kaste, North Frisian kastin), a word of uncertain origin.

The meaning "to form in a mold" is late 15c. In the sense of "to throw" it replaced Old English weorpan (see warp (v.)), and itself largely has been superseded by throw, though cast still is used of fishing lines (17c.) and glances (13c.).

From c. 1300 as "emit, give out;" also "throw to the ground;" also "shed or throw off;" also "calculate, find by reckoning; chart (a course)." From late 14c. as "to calculate astrologically." From late 15c. as "bring forth abortively or prematurely." From 1711 as "distribute the parts (of a play) among the actors." Of votes, from 1840, American English. To cast up is from 1530s as "compute, reckon" (accounts, etc.), late 15c. as "eject, vomit."

by c. 1200 as an emphatic form of Old English of (see of), employed in the adverbial use of that word. The prepositional meaning "away from" and the adjectival sense of "farther" were not firmly fixed in this variant until 17c., but once they were they left the original of with the transferred and weakened senses of the word. Meaning "not working" is from 1861.

Off the cuff "extemporaneously, without preparation" (1938) is from the notion of speaking from notes written in haste on one's shirt cuffs. In reference to clothing, off the rack (adj.) "not tailored, not made to individual requirements, ready-made" is by 1963, on the notion of buying it from the rack of a clothing store; off the record "not to be publicly disclosed" is from 1933; off the wall "crazy" is 1968, probably from the notion of a lunatic "bouncing off the walls" or else in reference to carom shots in squash, handball, etc.