Slice the ripe peaches into thin wedges using a chef's knife on a clean cutting board, revealing the vibrant orange flesh.
Cut the seedless watermelon into uniform cubes, approximately 1-inch in size, and place them in a large mixing bowl.
Add the sliced peaches to the bowl with watermelon. Finely chop the fresh mint leaves and sprinkle them over the fruit mixture.
Using a citrus juicer or hand-held lime squeezer, extract the juice of one lime and pour it evenly over the fruit. Gently toss all ingredients with a large spoon to combine until the lime juice coats the fruit evenly.
Arrange the fruit mixture on a serving platter, ensuring a colorful and even distribution of peaches and watermelon, garnished with a few whole mint leaves for presentation.