If you don't get every last root it will just resprout and you will probably end up with more plants than before your ripped it up. Mint spreads underground and a fence won't do anything. It can spread quite a distance too, like underneath a cement sidewalk before it pops up again. If you don't want it to spread all over the place you must either have a deep underground barrier around it or plant it in a pot. When planted in a pot the bottom must not touch the ground or the roots will escape out of the hole in the bottom. Although most mint is propagated by cuttings it can reseed itself and spread that way too. The only fool proof way to grow mint without it eventually taking over IMO, is to grow it indoors