Green’s Dictionary of Slang

1. to frustrate, to destroy.

1966		H.S. Thompson letter 25 Dec. in Proud Highway (1997) 595: The representative from Brooklyn [...] did all he could to stymie the merger in Congress.
1970		‘Red’ Rudensky Gonif 5: The putum situation didn’t stymie me for long.
1999		K. Sampson Powder 471: He decided to call Mr Hotshot there and then and stymie any lingering hopes he might have of rescuing this ‘situation’.
2019		C. Hammer Silver [ebook] ‘Technically, Mandalay could still stymie it [i.e. a deal]’.

2. (US campus) to deprive others by taking the last of anything.

1987

Eble Campus Sl. Oct. 6: stymie – take the last of anything: Sure, stymie my beer like you paid for it, you tramp.