Green’s Dictionary of Slang

1. (US) to speak in an aggressive manner.

1911		T.A. Dorgan in Zwilling TAD Lex. (1993) 81: The talker tore off the chin goods yard by yard.
1912		R.W. Brown ‘Word-List From Western Indiana’ in DN III:viii 592: tear off, v. To utter violently.

2. to snore.

1943

R. Llewellyn None But the Lonely Heart 307: Even if Ma been having her little forty after dinner [...] there was always a bit of a row going on somewhere, even if it was only her tearing it off up there, making a low, shaking sound as come through the floor and nigh shook the place.