Well it will - needs to be contained with a barrier inserted vertically into the soil 18 inches down. Pull up anything you find - you'll never get rid of it all anyway.

I grow mine in a container on the patio I tried a bottomless bucket in the garden once but it escaped. I agree pull up any you see as it spreads and spreads.

Ugh I also have mint taking over one of my beds. It's by the house and mint is supposed to keep ants away, so I'm not too upset. I pull it up, chop it down and rip it out wherever I don't want it. Doesn't seem to hurt the supply.