When I have mint where I don't want it, I just dig or pull it up. I have to be vigilant to remove the "resprouts" but , eventually, I have success. I find oregano much more invasive than mint as it propagates by seed. It becomes a lawn cover in just a few years.
I, also, find that mint is very beneficial in my garden and I usually give it free rein. It protects my cabbages, etc. It bolsters my tomatoes and it makes lovely tea. I have a wide range of varieties planted throughout the gardens. It is also great for Indian or Middle Eastern dishes. I don't see it as invasive, I see it as a gap filler.