"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]