To exorcise is to cast out a devil or evil spirit, using prayer and other religious tools. You're probably familiar with the name of the person who does this: an exorcist. Don't try to exorcise a demon yourself. Call an exorcist.
One way to remember the word exorcise is that it sounds like "exercise," which means to work out or train your body or mind. Casting out devils is hard work, so be sure to exercise before you exorcise. A boxer doesn't box without exercising first. And an exorcist doesn't exorcise without getting ready first either. The devil is a tough opponent, so you'd better get warmed up before you try to exorcise him from that little girl.