Grate the radishes on a box grater. Place the radishes in a paper towel and squeeze out the liquid. In a medium bowl, combine the radishes, garlic, yogurt, olive oil, lemon juice, scallions, mint, 1 1/2 teaspoons salt, and 3/4 teaspoon pepper. Cover, and refrigerate for at least 30 minutes or for up to 12 hours.