Green’s Dictionary of Slang

1. (Aus. Und.) to reject, to abandon.

1993

Smith & Noble Neddy (1998) 100: Bill, you are too dangerous, talking on the phone all the time. Pull up or I will have to drop off you for good.

2. (Aus.) to stop doing something.

1985

R.G. Barrett You Wouldn’t Be Dead for Quids (1989) 153: [He[ head butted him across the bridge of his nose, not hard enough to knock him out but enough to give him the drum to drop off.