Grate orange peel and remove leftover peel and pith. Separate orange into 8 segments.
Combine grated peel, orange juice, teriyaki sauce, mustard, honey, garlic and pepper in a bowl.
Cut beef into 1″ cubes and place in a resealable plastic bag. Add oranges, mushrooms, onions and half of marinade to beef in bag.
Seal bag and refrigerate overnight. Refrigerate remaining marinade for sauce.
Drain marinade from beef and discard.
Alternately thread beef, oranges and vegetables on to 4 metal or water-soaked wooden skewers. Grill on medium heat for 15-18 minutes or until the meat reaches desired doneness and vegetables are tender.
Combine cornstarch and water in a saucepan until smooth. Stir in reserved marinade. Bring to boil and stir for 2 minutes.