Calling The Police To Remove Unwanted Person From Property?

Location: Georgia

I am asking on behalf of my mother, as I recently moved out of her home. My younger sister (who is 23) has recently been hanging around with a much older man (my guess is that he is ~30-35). She still lives with my mom. At first, the man would come and go, but for the past few weeks he has been staying pretty much full time. As far as I understand it, he is homeless.

My mother and this man do not get along at all. She has been telling my sister that she does not want him at her house, but my sister continues to let him come around. I met this man for the first time today, and it is extremely clear to me that he is mentally unwell. My sister has been diagnosed with a few mental disorders and suffers from extreme paranoia, and this guy just feeds into it and is making her worse by the day. He has convinced my sister that my mother needs an exorcism, and that random household objects in her room have “bad energy,” causing my sister to throw out and pile up junk and furniture in the backyard.

Within the first couple of minutes of talking to this guy, I felt so much dread and anxiety. My mom told me she locks herself in her room due to fear. I am also afraid; I feel like I am in the beginning of a story that has a very bad ending.

My question is, can my mother have the police come and remove the man? She is the owner of her home, and has never given him permission to be on the property.

Secondly, what steps should my mother and I take to ensure he does not come back around?