As expected, the phrase announces that the speaker intends to both kick bubblegum and chew ass, only to express regret that he is all out of ass to chew. Cue furious bubblegum kicking.
You think you’re the shit, huh, pal? You think you got what it takes? Well let me tell you this: I’m here to kick bubblegum and chew ass…and I’m all outta ass.