The humorous Irish- and British-English phrase to extract the urine from (or out of) is a polite variant of the slang phrase to take the piss out of, meaning to tease or ridicule.

Similarly, the humorous British- and Irish-English phrase to extract the Michael (or the michael) from (or out of) is a polite variant of the informal phrase to take the mickey out of, meaning to tease or ridicule.

The earliest occurrences of the phrase to extract the urine from (or out of) that I have found are as follows, in chronological order:

1-: From a letter to the Editor, published in the Sunday Independent (Dublin, County Dublin, Ireland) of Sunday 12^th April 1987:

Sir—I would like to preface this epistle by expressing my sincere admiration for Mr. Hugh Leonard’s wizardry with the English language. Just by reading and learning from his column every Sunday, his writings have inspired my own literary ambitions in many ways: for example, I have decided to never split an infinitive from now on; nor will I ever again use a preposition to end a sentence with. (And, indeed, I will certainly never begin a sentence with a conjunction.)
However, if I may be so bold, I must question Mr. Leonard’s mastery of the laws of probability. He asks (in his column of April 5): “Supposing you toss a coin and it comes down heads five hundred times in a row, what are the chances that it will come down tails on the five-hundred-and-first toss?” After this, Mr. Leonard avers that if one hesitates before replying, one will die poor, “for the answer is: evens”. I disagree. I would respectfully submit that if a coin comes down heads five hundred times in a row, then the probability must be that the said coin is defective (tail-heavy?), and that the likelihood is that it will also come down heads on the five-hundred-and-first toss—KEVIN COLLINS, Bun An Chnuic, Rose Hill, Lee Road, Cork.
P.S.—My present wife advises me that the laws of probability also state that perhaps it is unwise to try to extract the urine out of Mr. Leonard; and so it is not without a little trepidation that I pen this—my first—letter to you!—K.C.

2-: From the column Eddie Holt on TV, published in the Irish Independent (Dublin, County Dublin, Ireland) of Saturday 12^th January 1991—the following is from the review of Challenging Times, an inter-university quiz show produced by, and broadcast on, RTÉ (Raidió Teilifís Éireann):

The pseudo-hysterical supporters however contrasted starkly with the austere grey set which bespoke pretension.
‘Neath classical arches supported by ionic columns (the characteristic ram’s horns decorations of which comprised of gaudy purple neon!) the students—especially the Trinity ones—looked intensely student-like. For image, if nothing else, Trinity is going to take some beating.
Think for instance of the rig-out of Vincent Piat-Kelly. In spite of the heat of studio lights, Vin wore enough clothes to feel perfectly safe about attempting an expedition to the South Pole. Perhaps like wally Paul he was extracting the urine . . . from himself. I wonder does he frequent The Bailey?

3-: From You’ve no taste Jonathan, a television review by Lynda Gilby, published in the Sunday Life (Belfast, County Antrim, Northern Ireland) of Sunday 22^nd December 1991:

If Wednesday’s Tonight With Jonathan Ross is anything to go by, we’re in danger of merely replacing one form of tasteless patronage with another.
Urged on by an audience which he appeared to have bought by the yard from Rent-A-Yob Mr Ross first extracted the urine from an unassuming, champion turkey-plucker, Mr Pilkington.
[…]
Mr Ross then announced with a flourish, the world premier of the latest adventures of the Gold Blend couple, asking: “After nine adverts, will he finally get to play hide the sausage?”
He didn’t and after the screening Mr Ross, ever master of that exquisitely sensitive instrument, the English language, insiively [sic] commented: “They never get round to shagging, do they?”

4-: From the column The Beard on the Box, by Keith Dufton, published in the Sunday Sun (Newcastle-upon-Tyne, Tyne and Wear, England) of Sunday 12^th January 1992:

DUFTON’S DUFFER

I’M not sure if the cast, producers and writers of Dysentery (BBC-1, Wed and Thurs) were extracting the urine out of themselves, us or both and don’t really care which as long as they don’t try this trick again.

5-: From Why the afterlife has little to recommend it, by Lynda Gilby, published in the Sunday Life (Belfast, County Antrim, Northern Ireland) of Sunday 5^th June 1994—Rory Bremner (born 1961) is a Scottish comedian and satirical impersonator:

Yet another book, Little One, by a lady called Ann Walker has just been published loaded with gobbledegook warnings from the ether about the future of our planet if we don’t pull our environmental socks up.
I’m not entirely sure I fancy the idea of an afterlife. On present showing, Heaven has little to recommend it. One can only presume that, there, Oscar Wilde will be stuck for an epigram, Mozart will be tone deaf and Errol Flynn will harbour all the sex appeal of a vat of cold cabbage.
Either that or the place will be populated by one huge celestial Rory Bremner who will have been extracting the urine from his intermediaries on earth for all these years.