A "mule kick" is usually a sign of a hit. What kind of broadhead were you using? I ask this because I've killed several buck that reacted the same way yours did while using a Magnus Stinger 2 blade. Ran a few yards, stopped and started walking again. Went a bit farther and fell down. Could be your arrow did deflect and you hit farther back then you wanted. You should have marked where you last saw him and went there to look for and blood or other sign.