Place spaghetti squash cut-side down in a baking pan. Pour in about 1 inch of water. Cover pan with aluminum foil.
Bake in the preheated oven until tender, 30 to 45 minutes. Remove from the oven, uncover, and cool until easily handled, 5 to 10 minutes. Use a fork to scrape insides of squash into spaghetti strands.
Heat olive oil in a large skillet over medium heat. Add onion; cook and stir until translucent, about 5 minutes. Add beets; cook and stir until slightly softened, about 5 minutes. Stir in green tomatoes, tomatoes, and zucchini. Simmer until beets are tender and tomatoes are soft, about 15 minutes. Season with salt and black pepper.
Serve stewed beet mixture over spaghetti squash strands.