Either a penis that has been inserted into a dirty ass, or a 300yard drive on the golf course that lands on right in the garden spot.
Aaron's meat puppet became a super stanky meat puppet when you rammed his cock into Debbie's dirty ass.
or
Mark just unloaded his driver and put his golf ball right in the clown's mouth; 300 yards and in the garden spot, thus giving the ball a stanky meat puppet.
This is a phrase that a gentleman may use to indicate that he is about to masturbate (referring, of course, to the penis as being a metaphor for a puppeteer's hand, with the female being the puppet).
Now with your kind permission, madam, I would like to retreat into the back room and engage in shaking hands with the puppet master. I shan't be long.
Jenkins was feeling very horny yesterday, as he hadn't participated in shaking hands with the puppet master since the weekend.
Also another name for a "woman." It happens when omeone at a bar is describing their dating life, describing the female gender as being difficult to understand, like a Chinese finger puzzle. Then a drunk guy across the bar says, "a Chinese fist puppet?"
You: I went on a date with her, but I just don't understand. She's like a Chinese finger puzzle.
Drunk Guy: What's a Chinese fist puppet?
You: That's funny, but that's not what I said. This needs to go on Urban Dictionary.