Cut beef across the grain into 1/4-inch thick strips.
Combine teriyaki sauce and sugar in measuring cup, stirring until sugar dissolves. Remove 3 tablespoons of mixture and pour over beef in large plastic food storage bag. Press air out of bag; close top securely. Turn bag over several times to coat pieces well. Marinate 15 minutes.
Meanwhile, add enough water to remaining teriyaki sauce mixture to measure 2/3 cup; blend in cornstarch. Heat oil in large skillet over heat; add beef and saute 1-2 minutes.
Add teriyaki sauce mixture. Continue to cook, stirring, about 1 minute, or until sauce boils and thickens slightly. Spoon beef and sauce over rice in large individual serving bowls. Serve vegetables on the side, if desired.