Can Christians divorce over verbal abuse?

Abuse does not have to be physical to be damaging. Emotional and verbal abuse is just as terrible and painful as physical abuse. Just because you cannot see the hurt does not mean the hurt is not there. If your mother wishes to leave him, then by all means she should. In fact, going by what you're written here, she should get away from him as quickly as possible. No one should ever have to live with any kind of abuse.