Whisk orange juice, vinegar, garlic, salt and pepper until combined. Slowly whisk in oil. Divide dressing mixture into two equal portions. Preheat barbecue to medium-high.
Insert a skewer through the side of each red onion slice to hold rings together. Brush one portion of dressing mixture over vegetables. Grill vegetables, turning as needed to prevent scorching and removing individual pieces as they are done, until all the vegetables are cooked, 15 to 20 min. Cool slightly. Chop larger vegetables into bite-size pieces. Remove skewers from onions and separate into rings.
Toss vegetables with salad greens and reserved dressing mixture. Sprinkle with feta and mint.