Trim fat from beef roast. In 12x8-inch (2-quart) glass baking dish or large resealable food storage plastic bag, combine all remaining ingredients; mix well. Add roast; turn to coat. Cover dish or seal bag. Refrigerate 6 hours or overnight, turning once or twice, to marinate.
Heat gas or charcoal grill. When grill is heated, remove roast from marinade; reserve and refrigerate marinade. Place roast on gas grill over medium-low heat or on charcoal grill 4 to 6 inches from medium-low coals. Cover grill; cook 50 to 75 minutes or until of desired doneness, turning once and basting with reserved marinade during last 15 minutes of cooking time. Discard any remaining marinade.