Dig mint out every time you see it growing where you don’t want it. Use a trowel for small clumps and a shovel for larger areas. Be sure to get all of the roots.
Pull mint out by hand. Grab the base of the plant and pull gently to ensure getting the entire strand that spreads just below the soil surface.
Stop watering the area where your unwanted mint is growing. Also, cover the area with a layer of clear plastic: this technique is called solarization. It will “cook” the soil, preventing most plants from growing.
Combine 2 cups salt, 1 tsp. dish soap and 1 gallon of white vinegar in a bucket. Pour this solution over an area that is no more than 3-by-3 feet where your unwanted mint is growing. Repeat this application every other day until the mint dies.