What does Mario say when he's throwing Bowser?

He's saying "So long(-a), Bowser".

You can hear the audio clip without the background music on The Mushroom Kingdom. Basically, it is just saying "So long, Bowser" with a Mario affectation.

According to the Mario Wiki, Mario says: "So long King Bowser!"

According to Mario’s voice actor Charles Martinet himself, he is saying: “So long kinga Bowser!”