How do you dispose of an old notary stamp?

You must turn it over to the Sectary of State in some states.

Other states require you to destroy it yourself.

I have a self inking rubber stamp so when it comes time, I just separate the rubber stamp part from the stamper (which is surprisingly very easy) and cut it up with scissors. You could also burn it. I've heard of running it over with a car but I suspect that will not damage the rubber stamp enough. The main thing is destroying the part that makes the impression well enough so it cannot be used.