Green’s Dictionary of Slang

(drugs) any form of tourniquet, e.g. a belt or bandanna, used to isolate the vein into which a drug is to be injected; also attrib.

1971		E.E. Landy Underground Dict. (1972).
1992		Bentley & Corbett Prison Sl. 82: Tie-Off also Tie A device used in a tourniquet fashion to enlarge a person’s vein making it stand out and move close to the skin surface.
1997		L. Pettiway Workin’ It 190: Then you take your tie if you need to tie.
c.2003		D. Vrij ‘Tying Off’ on Inter-zone.org 🌐 Dalton pulled off his belt and lashed it around the steering wheel, had he been out the car it would have been around his right leg, he was going for the wrist hit a definite tie off move.