It looks a little like anthracnose. If the weather has been wet an humid, it could happen. The spores splash up from the soil. You can pick off the leaves. But for me mint is easier to replace. I would get rid of the mint and the soil, since it will contain the fungal spores for a long time. I would wait for a while before getting new plants. You want to make sure the spore count is down and everything has a chance to dry out. Get clean plants in a clean pot and preferable put it in a different location.