Green’s Dictionary of Slang

(Aus.) an expression of dismissal.

1924		(con. WWI) A.G. Pretty Gloss. of Sl. [...] in the A.I.F. 1921–1924 (rev. t/s) n.p.: blow off. Go away, clear out.
1981		Eble Campus Sl. Mar. 1: blow off – exclamation meaning leave me alone or shut up about a particular subject.