Green’s Dictionary of Slang

an excl. of dismissal.

1865		J. Horrocks letter in My Dear Parents 31 July 147: He is a mean skunk. ‘Let him rip.’.
1877		Columbian (Bloomsburg, PA) 2 Feb. 1/8: He’s going to blow the old thing out and bust her up, let her rip.
1895		‘Banjo’ Paterson ‘Johnson’s Antidote’ Man from Snowy River (1902) 146: Get a pair of dogs and try it, let the snake give both a nip; / Give your dog the snakebite mixture, let the other fellow rip.
1900		Bulletin (Sydney) 7 Apr. 31/2: Oh, let the beggar rip; he’ll hang as well that way as standing.
1907		Gem 23 Mar. 10: Let her rip!
1914		Daily Book (Chicago) 2 June 32/2: Colonel says that he ate monkys on his trip / That raises quite a question, folks; / I guess I’ll let ’er rip—.
1924		Galsworthy White Monkey 270: ‘What shall we do about him?’ ‘Let him rip, my dear.’.
1971		H.E. Roberts Third Ear n.p.: let it rip don’t bother; let it go; skip it.