Combine first 6 ingredients in a large bowl, stirring well with a whisk. Add 3 tablespoons mint and 3 tablespoons oregano.
Add zucchini slices, tossing gently to coat. Let stand at room temperature at least 15 minutes, stirring occasionally.
Remove zucchini from bowl, reserving marinade. Place zucchini slices on grill rack; cover and grill 3 minutes on each side or just until tender. Arrange zucchini on a platter; drizzle with reserved marinade, and sprinkle with remaining 1 tablespoon each of mint and oregano. Serve warm or at room temperature.