The Puppeteer is a very wacky individual similar to his voice claims and how they behave when presented with stupid situations or situations that seem big. He has a wide range of emotions but usually dumbs them all down into comedic fourth wall breaks, yknow, the classic villain sidekick. He is far from comedic relief but he does take his job considerably less serious than most of the characters that appear in the show.

The Puppeteer, also referred to as "Puppet", is usually talking smack or having fun on jobs that go wrong. However he can play the part of a hardy body guard to Michael, he has the ability to shoot metal tentacles from his back and pop off his head for some reason. Both these things give him an edge on being able to instigate fear into the hearts of anyone Michael does business with. His craziness makes people wary and he can be visibly seen playing many roles in Michael's narrative. He's a wildcard so to speak.
If given the part you need to be able to portray both a serious side and wacky side, he likes to play with his victims but if they aren't giving him the information he needs, he's happy to put on the serious face until they talk. 

The voice lines here give you a general idea of his common portrayal amongst Michael and the rest of the team, still in the show it will vary, so play with other lines that aren't listed here if you wish.
You can also use lines from Invader Zim that he says in the claim video or any from the show in general, I'd love to hear it! Any Richard Horvitz character you may be fond would be cool as well. If you have any questions or want to request more lines then please feel free to ask! I apologize if it's not very clear, I tried to describe him best I could. 

Side note: If the dynamics of him and Michael's relationship would help you discern anything, think of them as Roman Sionis and Victor Zsasz from "Birds of Prey".