Um... I just looked it up. Rather gruesome little puppet-plays. Apparently Punch usually ends up killing most of the other characters in the show, all the while very pleased with himself. Several sources say it is indeed the source for that phrase.
I'm a pirate who doesn't do anything! I mean, I've never kissed a chipmunk... I don't look good in leggings... I've never been to Boston in the fall...
And now a new one for the song..."And I've never killed a puppet..."