I just bought some stamps from Art Neko and while browsing their site found this great tip:
"Many stampers have
found that cutting their stamps out with a scroll saw is a quick and easy
option, especially when the stamps are on a sheet of mounting foam. For anyone
who sews it is like feeding fabric under the foot of the sewing machine. We use
a saw blade with 18.5 teeth per inch for trimming our stamps."
I prefer unmounted stamps since there is usually a pretty decent cost savings vs. mounted ones. I've always cut mine out by hand after attaching to cling mount. It never occured to me to use a scroll saw though - love that idea.