I think the usage of the word "mutt" depends entirely on whoever is saying it.
For example, when people say that their "designer dogs" are the best, I do use "mutt" in the derogatory sense. Which, now that I look back on it, I suppose isn't wise, since it's in no way the dog's fault for being what it is.
However, when I talk to my dog, I call him a mutt, but I say it in an affectionate way. "I love you, you stupid mutt" is what I usually say whilst petting him and giving him treats. I don't think he has any clue what I'm saying. Hell, I've even said a bunch of curse words in a soothing, soft voice, the same I'd use if I was saying "You're such a lovely dog" and he doesn't seem to mind. Just wags his tail like it's some grand thing.
Anyway, it depends on the person if the actual word is bad. Just like everything else. I don't think the word "ignorant" is a bad word. It simply means one who does not know, or someone who is uneducated in a certain subject. Using myself, I'm completely ignorant when it comes to Mathematics. I can't divide to save my life, and I'm out of high school already.
Gah, once again, I've written an answer that's far too long and has gotten totally off-subject. Well, you get my point. It's not the word, it's the person saying it.
xo VIE xo