If you go to Petfinder there’s an area to the left where you can specify breed mixes. Of course you can’t be totally certain but the classifications in the listings are estimates by the shelter workers based upon the dogs looks and temperament.
BTW. The reason why purebred breeders don’t do mutts is because the shelters are already overflowing with mutts from irresponsible owners too lazy/ignorant to spay/neuter their pets. To add to that would be very irresponsible.
You might desire a very specific breed mix mutt, but then what becomes of the other puppies in that litter ? That’s right. They likely take up shelter space and other dogs die needlessly.
Responsible breeders are usually all about maintaining the standards of their chosen breed and ensuring that the pups go to good responsible homes. They aren’t in it just for the money since there are far more efficient ways to make a lot more money faster.
These breeders usually really love the dogs of their chosen breed so it’s done more for love than strictly money.
There is absolutely no reason for them to purposely breed mutts. Makes no sense at all aesthetically, morally or financiallly.