In a 5- to 6-quart slow cooker, whisk together the cider, tomato paste, flour, Worcestershire, and 1/4 teaspoon each salt and pepper. Add the sweet potatoes, onion, garlic, and rosemary and toss to combine.
Season the roast with 1 teaspoon each salt and pepper and nestle among the vegetables. Cook, covered, until the meat is tender, 6 to 7 hours on high or 8 to 9 hours on low.
Transfer the roast to a cutting board and slice. Serve with the vegetables.