If a child is physically abused by a parent using a sharp object and causes minor bleeding, is this considered a felony or a misdemeanor?

Each state in this country has its own statutes to determine whether the incident you have written about should be charged as a misdemeanor or a felony. Ultimately the final decision on the subject is to be determined by the trier of fact as to this criminal matter. I suggest that you consult with a criminal defense attorney about the matter sooner rather than later.