Cut beef actoss grain into strips, then into 1 1/2 " squares. Combine 2 T cornstarch, 1 T teriyaki sauce, sherry and garlic in medium bowl, stir into beef, and let stand for 30 minutes.
Combine water, remaining 1 T cornstarch, 3 T teriyaki sauce, vinegar, and red pepper flakes and set aside.
Heat 1 T of oil in a hot wok or large skillet over high heat. Add beef and stir fry for a couple of minutes until no longer pink. Remove from heat.
Heat remaining 1 T oil in same pan. Add green pepper and other vegetables, reserving mushrooms and onions until the very end. Stir fry these for 4 - 5 minutes.
Add beef, teriyaki sauce mixture, mushrooms and onions and cook while stirring until sauce thickens and boils.