… can take up to three to four hours to smoke and require basting once per hour. ... Can I do this with a rump roast? Jeff Smuth April 2, 2020 at 7:44 am - Reply. When you get a hankering for smoked beef, try my recipe for tender and juicy smoked chuck roast pulled and chopped to perfection and served on a bun or as it is. The beauty of smoking a large cut of beef is that the cooking essentially takes care of itself, with minimal involvement by the backyard chef. A rump up to 6 lb. Smoking a rump roast on an outdoor cooker produces flavorful, tender beef with a tantalizing, smoky aroma. Smoked Rump Roast .....it came out .....MMmmmmm!!!!! Taking it up to 205*F would let the meat be Pulled.