In a large bowl, whisk together the olive oil, vinegar, cumin, coriander, cayenne, salt, and pepper.
Trim off excess fat from the steak. Cut into 1½-inch cubes and place in a large bowl. Cover and let marinate for 30 minutes at room temperature.
Meanwhile, make the yogurt sauce: in a small mixing bowl, whisk together the yogurt, olive oil, lemon juice, garlic, mint, salt, and pepper. Cover and refrigerate until ready to serve.
Soak the wooden skewers for 10 minutes. Once soaked, thread the marinated meat, bell peppers, and onions onto the skewers.
Heat the grill over medium-high heat (about 400℉). Place the skewers on the grill and cook for about 4 minutes per side for medium or until the meat reaches your desired doneness.
Transfer the skewers to a plate and let rest for 5 minutes prior to serving.
Serve with warm pita, mint yogurt sauce, and more fresh mint for garnish.