Cut venison roast in half and rub with brown sugar. Place roast into a slow cooker and add the apple juice, soy sauce, and salt. Cover and cook on Low setting for 6 hours or until meat is tender. Remove meat from slow cooker, cover, and let stand for 15 minutes.
Pour drippings through strainer into medium sized bowl, return juices to slow cooker and discard material in strainer. In a small bowl, combine water and cornstarch until smooth; stir into cooking juices until well combined. Cover and cook on High until thickened, about 15 minutes. Slice meat and serve with gravy.
