When someone has been mauled by a dog it means that the person was injured by the dog through attack by the dogs claws or teeth and is usually injured pretty badly.
Mauled by an animal just means that the animal injured the person or child with it's teeth or claws.
The animal usually tears into the persons skin and causes injury enough to where the person needs stitches or other medical attention.
Basically being mauled by an animal is getting injured more than just being bitten by the dog or other animal.