v.1. To dismiss or refuse something or someone by waving the hand or arm: The celebrity waved off our invitation to join our group. The bus driver waved us off and refused to stop.
2. Sports To cancel or nullify something by waving the arms, usually from a crossed position: The official waved off the goal because time had run out. The referee waved the penalty off after reviewing the play.
3. To acknowledge someone's departure by waving the hand or arm: We went down to the train station to wave off the politician. We waved our guests off at the airport.