Rump roast, like chuck roast, is a very heavily exercised part of the cow, full of marbling and collagen. 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. Step 2: Set up and preheat your smoker to 250°F. Taking it up to 205*F would let the meat be Pulled. Cooking rump roast, chuck roast, or brisket is a simple matter of putting it in the oven, roaster, or slow cooker and taking it out hot and juicy a few hours later. This is a great way to make that roast. If using an electric smoker, fill the water bowl half way and place wood chips in the tray. Regardless of which you use, the right smoked beef rump roast or chuck roast should always be fatty and well-marbled. Smoking a rump roast on an outdoor cooker produces flavorful, tender beef with a tantalizing, smoky aroma. Smoked Bottom Round Roast – Instructions. It can be just as delicious as chuck roast, though chuck often provides shoppers with a more affordable purchase. Smoked Rump Roast came out .....MMmmmmm!!!!! Step 1: Remove the roast from the refrigerator 40 minutes prior to cooking and allow it to come to room temperature. can take up to three to four hours to smoke and require basting once per hour. The only reason to take Beef to 180-190*F would be to breakdown the Connective Tissue in a very tough piece of meat like a Brisket or a Chuck Roast.