Stephenie Meyer's description of women of color (Eclipse):
But of course, a brown man’s destiny is to suffer to save the white woman her tears.
In contrast, "dog" and "mongrel" are belittling terms for a 6'7" werewolf. A comparable insult for vampires might be "wormfood" (because of their dead bodies), "soul-stealer," or "murderer." In other words, something that acknowledges how Twilight's vampires are generally evil or inhuman.
For more on the subject, see Quileute Werewolves in Twilight.