First, let's establish which mint beetle you mean - if yours are green, then they're native ones - if they're blue, then the RHS wants to be notified that you've got them. This one's a new invader and they want to track its progress round the country.

If there aren't many, then its possible to pick off larvae and beetles, but it sounds like you've a heavy infestation - spray with Westland Fruit and Vegetable BugKiller or Bayer Ultimate Fruit and Veg Bugkiller. You need to leave 7 days minimum between spraying with either of these products and picking leaves for food use.