Could my child have a mental disorder? Hurts our cat biting ear.

Maybe. How old is your child? A young child who is starting to bite may not realize that it hurts people and animals. If you child is old enough to know this, do check with your child's doctor. Your child could be acting out from a variety of issues- stress, changes in the household, illness, or anxiety.
Maybe. Any child who hurts animals should be evaluated by his doctor and /or a therapist.