Yes. If it is truly an issue and it can be shown to a judge, that visitation may be limited to supervised only. It is very rare that a Court will deny all visitation.
Please note that this response is based upon the limited information available in the question. In addition, it is not intended to create an attorney/client relationship and is offered only as general information and not as legal advice.
I agree with Attorney Allen. Due to your concerns of abuse, you should consider asking the court to appoint a Guardian ad Litem to represent the interests of your child. While it may be hard for you to convince the judge of emotional and mental abuse, if the Guardian ad Litem investigates and in their neutral position find the abuse you have seen occurred or continues to occur, they are likely to recommend only supervised visitation, and possibly counseling to see if the father can correct his interactions for the well being of the child.
REMEMBER, my answer to your question is for general informational purposes, as I don't know all the facts and circumstances relating to the specific person(s) and situations involved. You should always consult with an attorney prior to making any legal decision. This response does not constitute legal advice or create an attorney/client relationship. For specific information regarding your case, call my office at 703-499-5843 to schedule a free 30 minute consultation.