Some people have purebred dogs, but you might have a mongrel — a mutt that is part this, part that, and part the other thing (but to you he's a 100 percent dog and your best friend).
Mongrel has the Middle English root word mong, which meant "mix." If you use the word mongrel to refer to the mixed ancestry of a dog or other animal, you may or may not intend to be insulting. If you refer to a human as a mongrel, you are definitely making a pejorative comment about that person's origins. In this use, it is considered an insult.