A "mickey-take" is the act of "taking the
mickey out of"
someone or
something, which means to
tease, to
mock, or to otherwise make seem
foolish. Its use predominates in the
United Kingdom, and in
Australia.
Its origins lie in Cockney Rhyming Slang, where "mickey" associates with "bliss" (the reason for which nobody knows anymore) which rhymes with "piss". So, when someone "takes the Mickey", or does a mickey-take, they
"take the piss", or do a piss-take, and thereby ridicule another person, seriously or in jest.
My first experience with the expression was when wertperch mentioned it to me in a private message. It is alternately written or spoken as "michael-take", "mike-take", and "micky-take".