Coat a large pot with cooking spray and place over medium heat. Cook and stir onion and mushrooms in the hot pot until the onion is translucent, 5 to 7 minutes. Break ground beef into small bits into the pot; cook and stir until beef is completely browned, 7 to 10 minutes. Drain grease from the pot.
Stir water, alphabet soup, mixed vegetables, tomato sauce, orzo pasta, basil, oregano, garlic powder, salt, and pepper with the ground beef mixture; bring to a boil, reduce heat to medium-low, and cook at a simmer until the orzo is tender, about 30 minutes.