Green’s Dictionary of Slang

dot n.⁵

In phrases

go off one’s dot (v.) [dotty adj.]

to go mad; thus off one’s dot, mad.

1889–90		Barrère & Leland Dict. of Sl., Jargon and Cant.
1894		Albert Chevalier ‘Our Court Ball’ 🎵 Well, there it’s superb! ’Nuff to make a bloke go clean orf ’is dot.
1894		Truth (Sydney) 15 Apr. 1/6: Deceased was unmarried, and had gone off his dot over a barmaid.
1898		Munsey’s Mag. 18 268: Betty said: ‘Pon my honor, though, that man must be off his dot,’ and the lady in blue went into convulsions of hysterical giggling.
1905		A. Binstead Mop Fair 50: A well-known ’Arley Street medical man, what went off ’is dot [...] an’ who is at present immured in a private ’ome for the potty.
1906		Sun. Times (Perth) 2 Dec. 4/8: The unions have gone off their dot.
1908		Magnet 29 Feb. 11: What makes you think that Vaseline has gone off his dot?
1917		Yorks. Eve. Post 17 May 4/3: I like books about artists and dreamers and anybody who is a little off his dot.
1929		J.B. Priestley Good Companions 366: I mun tell somebody [...] or I’ll be going right clean off me dot.