Heat a skillet over medium heat; cook and stir sausage, onion, and bell pepper in the hot skillet until vegetables are tender, about 5 minutes.
Whisk apricot preserves, cornstarch, soy sauce, vinegar, and ginger in a small bowl; stir mixture into sausage mixture. Cook and stir until thickened, about 5 minutes. Add pineapple chunks and tomatoes. Continue to cook and stir until heated through, about 10 minutes more.