go off v.

Old English gan "to advance, walk; depart, go away; happen, take place; conquer; observe, practice, exercise," from West Germanic *gaian (source also of Old Saxon, Old Frisian gan, Middle Dutch gaen, Dutch gaan, Old High German gan, German gehen), from PIE root *ghē- "to release, let go; be released" (source also of Sanskrit jihite "goes away," Greek kikhano "I reach, meet with"), but there does not seem to be general agreement on a list of cognates.

A defective verb throughout its recorded history; the Old English past tense was eode, a word of uncertain origin but evidently once a different verb (perhaps connected to Gothic iddja); it was replaced 1400s by went, past tense of wenden "to direct one's way" (see wend). In northern England and Scotland, however, eode tended to be replaced by gaed, a construction based on go. In modern English, only be and go take their past tenses from entirely different verbs.

The word in its various forms and combinations takes up 45 columns of close print in the OED. Meaning "cease to exist" is from c. 1200; that of "to appear" (with reference to dress, appearance, etc.) is from late 14c.; that of "to be sold" is from early 15c. Meaning "to be known" (with by) is from 1590s; that of "pass into another condition or state" is from 1580s. From c. 1600 as "to wager," hence also "to stand treat," and to go (someone) better in wagering (1864). Meaning "say" emerged 1960s in teen slang. Colloquial meaning "urinate or defecate" attested by 1926, euphemistic (compare Old English gong "a privy," literally "a going").

To go back on "prove faithless to" is from 1859; to go under in the figurative sense "to fail" is from 1849. To go places "be successful" is by 1934.

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.