According to folk-comedy duo Flight of the Conchords, Mutha'uckas are people who " 'uck with your shi-", such as a racist fruit vendor, or people who work at the bank.
it can also be a thing, such as "mutha uckin rent"
1) I pay my mutha'uckin' rent fortnightly
Mutha'uckas at the bank trying to play me
2) The mutha'ucka runs a racist 'uckin' grocery
The mutha'ucka won't sell an apple to a Kiwi