Heat a large pot over medium heat. Cook and stir ground beef and ground turkey in the pot until completely browned, 7 to 10 minutes. Stir onion into the meat mixture; continue to cook and stir until the onion is translucent, about 5 minutes. Drain fat from the pot and return to medium heat.
Pour water and tomatoes into the pot. Season soup with garlic powder, sea salt, basil, and black pepper. Stir beef base through the soup. Add frozen mixed vegetables to the pot; stir.
Bring the soup to a boil, reduce heat to low, and cook, stirring occasionally, until the vegetables are cooked through, 20 to 30 minutes.