Green’s Dictionary of Slang

amputate one’s mahogany v.

also amputate, amputate (one’s) logwood, ... (one’s) timber
[synon. for cut (one’s) stick(s) v. (1)]

to run away.

[UK]Age (London) 7 Apr. 5/1: Melbourne swears that the minute Prince Alexander of Russia occupies two of Mivart's houses with his thirty subordinates in sable, he will amputate his mahogany from Buckingham Palace.
[UK]Hull Packet 5 May 3/6: He protested that mary had never behaved to him as a wife and that she had amputated her mahogany to such an extent going to a neighbour’s, that he had to do everything himself.
[Ire]Cork Examiner 16 June 4/4: The gin-drinking Dutch trooper [...] who amputated his mahogany at the Boyne.
[US]North-Carolinan (Fayetteville, NC) 18 Nov. 1/6: To leave [...] amputate timber.
[Aus]Bell’s Life in Sydney 20 Jan. 3/2: [He] amputated his mahogany in double quick sticks.
[UK]Fast Man 7:1 n.p.: [T]he Colonel, having denuded of its flowers the garden which had attracted him, amputated his logwood for Edinburgh.
[Aus]Bell’s Life in Sydney 18 Jan. 2/7: He had observed her amputating her tottering mahogany down George-street.
[UK]‘Ducange Anglicus’ Vulgar Tongue.
[US]Matsell Vocabulum 8: Amputate your Mahogany or Timber. Be off quick; away with you.
[UK]Hotten Sl. Dict.
[US]Trumble ‘On the Trail’ in Sl. Dict. (1890) 41: I must amputate like a go-away, or those frogs will nail me.
[Aus]‘Lela’ in Maitland Mercury (Aus./NSW) 2: In the rear of the house one of the gang of badnitti strode up to him. ‘Ye ain’t such an addle cove as to git egag cause you amputated the bandog and beat the scorn, are ye?’.
[UK]Farmer & Henley Sl. and Its Analogues.
[Aus]C. Crowe Aus. Sl. Dict 4: Amputate, to make off without delay.