Drain pineapple, reserving juices. Add enough cold water to juice to measure 1-1/2 cups. In a bowl, combine brown sugar and cornstarch. Gradually whisk in juice mixture until well blended. Stir in vinegar and soy sauce; set aside.
In a large skillet, stir-fry sausage, carrots and pepper until carrots are crisp-tender, about 6 minutes. Stir juice mixture; stir into skillet.
Bring to a boil; cook and stir for 1 minute or until thickened. Stir in pineapple; cook until heated through, stirring occasionally. Serve with rice.