Yup, both sides, too.
I've made up a cutter from a piece of steel pipe. 1 1/4" works well.
Grind/file the outside until the inside edge is very sharp.
Stick a piece of Gorilla tape to something sorta flexible, linoleum works well.
Cut the circle with that punch with a single blow from a hammer of some size.
Peel off the scrap(s), then the patch which may be up inside.
Circles seem to work best, as they don't fray at the edges.
Good luck Saskbucks.