Green’s Dictionary of Slang

blow off v.2

[blow off n.1 (1) / blow off steam under steam n.]

1. [late 19C+] (also blow it off) to release pent-up emotion.

2. [1910s+] to get angry (with).

3. [1970s+] (US gay, also blow off steam) to achieve orgasm.

In phrases

blow off at the mouth (v.) (also blow off at one’s head, blow off one’s mouth) [sense 1 + SE mouth/head]

[1940s+] to talk loudly or aggressively, to boast.