When these two words are misused, the mistake is probably due to misspelling or mispronunciation. Exercise means "something done or performed," "bodily or mental exertion," "to train, develop, or condition": "This is an exercise to strengthen one's back." "Exercise your mind or it will become slack." Exorcise, a verb only, means "to cast out," "to expel," "to deliver from": "The faith healer tried to exorcise an evil spirit from the sick man."
Dictionary of problem words and expressions. Harry Shaw. 1975.