piss off v.

"to urinate, discharge the fluid secreted by the kidneys and stored in the urinary bladder," c. 1300, pissen, from Old French pissier "urinate" (12c.), from Vulgar Latin *pissiare, of imitative origin. To piss away (money, etc.) is from 1948. Related: Pissed; pissing. Pissing while (1550s) once meant "a short time."

He shall not piss my money against the wall; he shall not have my money to spend in liquor. [Grose, "Classical Dictionary of the Vulgar Tongue," 3rd edition, 1796]

To piss money on the walls "throw money around recklessly" is attested from 1540s.

He who once a good name gets,

May piss a bed, and say he sweats.

["Dictionary of Buckish Slang, University Wit and Pickpocket Eloquence," London, 1811] 

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.

1929, "drunk," past-participle adjective from piss (v.). From 1946 as "angry," from piss off.