1) To defecate in a very forceful manner.
2) To defecate so much in the toilet, it is effectively "destroyed."
3) A violent, sometimes painful expelling of fecal matter, prone to leaving splatter marks in the bowl and/or on the underside of the seat of one's toilet.
Cartman: "I'm going to the bathroom!"
Kyle: "Dude, he's totally punishing your toilet!"