1. Set up your grill for direct grilling and preheat to high. If using a vegetable grate, preheat it as well.
2. Meanwhile, cut the zucchini and squash lengthwise into 1/4 inch slices. Arrange the slices on a platter and drizzle with the oil, turning the slices several times to coat both sides with oil. Sprinkle the slices on both sides with the garlic, oregano, mint, hot pepper flakes, and lots of salt and pepper. Let marinate for 15 minutes.
3. Arrange the squash slices on the grate and grill until nicely browned on both sides, 4 to 6 minutes per side. Transfer the squash to a platter and arrange in an attractive pattern. Garnish with lemon wedges for squeezing. Serve hot or at room temperature.