You'd just be spinning the chunk you broke off. The rest of it would sail on.
Law of conservation of angular momentum would cause the now smaller parts to fly off in different directions.
Thus you now have smaller chunks, many of which would no longer be a threat. The course change of these smaller parts would either take them out of the path of impact with earth or cause them to fall within another planets orbit or most likely, the suns. Further, the parts that remain on the impact trajectory would be smaller.