I can't believe none of my fellow lusophones has added our contribution to such worthy linguistic matter. I can't believe it's even closer to butter either, but that's a different pet peeve. Either way, Camões' language deserves better! And the World Cup is upon us, so you need to know what to say over here, or at least to your telly when your favorite footballer scores nicely.
First of all, the literal translation of "mutt's nuts" wouldn't have the British meaning here in Brazil, at least in the regions I am familiar with (the country is huge and there are very strange idioms and sayings in other regions that are not intelligible in others, so who knows...). But fret not, we do have an equivalent genital-based expression to provide; a very naughty language, (Braz.) Portuguese.
The literal translation could be "as bolas do cão" (the dog's balls, where ão is a sound that is allegedly exclusive from Portuguese, and sounds sort of like what you get if you say "uh" followed by a deep "mmm", quickly and very nasally). If you don't want to wrestle with the damn ão, you can use "cachorro", which is another word for dog, but that would make the saying much less snappy, admittedly. Also, if you want to keep the mutt (as in "of mixed-breed") element in the saying, use "vira-lata" (literally "turn-can", a dog who lives in the streets messing with trash cans to get food).
We have other ways to refer to the gonads, so you could also use "o saco" (the sac, scrotum) or
"os ovos" (the eggs) instead of "as bolas". I never promised it would be easy, or even less that it would be succinct. Not my style.
Now, the genital-based expression I promised earlier is "do caralho" (where "lho" is like the Italian "glio", i.e. something like "ly-oh" said quickly in English). It is somewhat NSFW (although we're not very shy with the swearing down here, and you might be surprised with what you can hear at work), and it literally means "of the cock", but not of the avian kind, obviously. When a Brazilian says something is "do caralho!", or the shortened version, "duca!", pronounced doo-kah, streess on the doo, as in booing, it means... it's the mutt's nuts. The species of the owner of the "caralho" is not specified here, but the meaning is still the same.