Green’s Dictionary of Slang

1. to defeat or disable in a contest; thus tie-up n., a defeat.

1818		Sporting Mag. II 11: [implied] He knobbed his adversary well, and floored him by a smart tye-up at the fourth buttonhole.
1890–1904		Farmer & Henley Sl. and Its Analogues.

2. to fight.

1928

J. Callahan Man’s Grim Justice 254: Don’t make any cracks about my church, or you and I’ll tie up.