Heat the oil and garlic in a small saucepan over low heat, just until the garlic is very aromatic, about 2 minutes. Remove from the heat.
Preheat a gas grill to high or let a charcoal fire burn down to white-hot. Brush the zucchini with some of the garlic oil and season to taste with salt and pepper. Grill the zucchini, skin side down, until it begins to soften, about 3 minutes. Turn and cook until tender, 3 to 6 minutes more, depending on the size of the zucchini.
Cut each zucchini half at a sharp angle into 2 or 3 pieces and place in a bowl. Add the vinegar, mint, and the remaining garlic oil. Toss well. Season with additional salt and pepper. Serve warm or at room temperature.