Whisk together olive oil, vinegar, lemon juice, 1/2 teaspoon salt, and 1/4 teaspoon pepper in a small bowl; set vinaigrette aside.
Halve and pit peaches. Cut halves into quarters. Remove core from stem end of large tomatoes; slice into 1/2-inch rounds.
Arrange peaches, tomatoes, cherry tomatoes, and celery on a serving plate. Sprinkle with remaining 1/4 teaspoon salt and pepper. Coarsely chop mint leaves; add to vinaigrette. Pour over salad, and garnish with mint sprigs.