What does it mean by "throw you around the floor"? Is he asking her to dance or something?

Native speaker’s answer
Rebecca
That's right! He's asking her to dance, but with a little bit of humor. The "floor" does refer to the "dance floor" where everyone dances in the room. It's a specific space for dancing. Ex: Everybody! Get on the dance floor. Let's dance. Ex: Do you see those two dancers? They're really tearing up the floor. => Dancing well, and a lot.