Green’s Dictionary of Slang

chute n.

(US) the rectum or anus.

[Aus]‘Salome’ in Mess Songs & Rhymes of the RAAF 25: Standing there with her arsehole bare / Waiting for some-one to slide in there / [...] / Fair up her fucking chute.
[US]R. Price Blood Brothers 151: But the best, Butler, the fuckin’ coup de grace a the whole night [...] we did it up the chute.
M.E. Dassad ‘Chickenhawk’ at [Internet] Ramon grabbed Karen’s ass cheeks and quickly thrust his dick balls deep into her chute, and grabbing her hips he began thrusting into her with incredible energy.

In phrases

down the chute (adj.) [SE chute, a narrow passage through which animals are driven for branding, shearing etc.]

1. (Aus. Und.) found guilty in court and thus imprisoned.

[Aus]Arrow (Sydney) 27 Nov. 4/3: A jury says that Bill is guilty, and a Judge sends him ‘down the chute’ for six months.
[Aus]Truth (Brisbane) 26 Dec. 20/3: In Brisbane Police Court last week [...] a pair of the city’s hardened lags went down the chute for a ‘sixer,’ for stealing.
[Aus]S.J. Baker in Sun. Herald (Sydney) 8 June 9/2: Then there’s [...] ‘down the chute,’ found guilty.
[Aus]N. Pulliam I Travelled a Lonely Land (1957) 232/2: down the chute – in jail.

2. (Aus. Und.) in fig. use, following the ‘road of crime’.

[Aus]Argus (Melbourne) 19 Dec. 8/1: Surely it's better to reform a man than to send him further down the ‘chute’ (the road of crime). The trip down the "chute" often starts in a so-called boys' home. I firmly believe that more damage is done in some of these homes than in any gaol.
up the chute (also up the shoot)

1. (Aus./N.Z.) useless, worthless, failed, in serious trouble.

[Aus]Baker Popular Dict. Aus. Sl.
[UK]W. Hall Long and the Short and the Tall Act I: If he’d have pulled the pins on one of them grenades we’d all of us been up the shoot!
[Aus]G.W. Turner Eng. Lang. in Aus. and N.Z. 108: New Zealand has some slang of its own [...] Up the chute.
[NZ]R. Morrieson Pallet on the Floor 49: You’re all up the shoot.
[NZ]McGill Dict. of Kiwi Sl. 117/2: up the chute worthless, stupid, wrong; eg ‘Sorry, chum, you’re up the chute on that one.’.
[Ire](con. 1945) S. McAughtry Touch and Go 139: If I ever stood a chance of keeping the job it’s up the chute now.
[NZ]McGill Reed Dict. of N.Z. Sl. [as cit. 1988].

2. see up the pole adj.2