1. Trim fat from roast. If necessary, cut roast to fit into a 3 1/2- to 6-quart slow cooker. Coat an unheated large nonstick skillet with nonstick cooking spray. Preheat skillet over medium heat. Brown roast on all sides in hot skillet.
2. Meanwhile, in the slow cooker stir together turnips, carrots, tomato sauce, red wine or beef broth, tapioca, salt, allspice, and pepper. Place roast to cover vegetables. Place squash on roast. Cover and cook on low-heat setting for 10 to 12 hours or high-heat setting for 5 to 6 hours.
3. Transfer roast and vegetables to a warm serving platter. Skim fat from tomato sauce mixture in slow cooker. Pass tomato sauce mixture with roast. Makes 6 (4 ounces cooked meat, 1/2 cup vegetables, and 1/2 cup gravy) servings.