I was making heart confetti and my paper level punch was stuck. I watched a YouTube video and it said to take apart the punch or use a hammer to pound on it. Instead, I decided to just stick my scissors into the center where the dot is sticking out and pushed it down. It released the stuck paper punch!
I haven't had another stuck paper punch since so I can't replicate at the moment though, but this worked for me!
Source: Personal experience