Smoked Bottom Round Roast – Instructions. Taking it up to 205*F would let the meat be Pulled. Step 1: Remove the roast from the refrigerator 40 minutes prior to cooking and allow it to come to room temperature. Regardless of which you use, the right smoked beef rump roast or chuck roast should always be fatty and well-marbled. Smoked Rump Roast came out .....MMmmmmm!!!!! can take up to three to four hours to smoke and require basting once per hour. A rump up to 6 lb. Smoking a rump roast on an outdoor cooker produces flavorful, tender beef with a tantalizing, smoky aroma. This is a great way to make that roast. 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. It can be just as delicious as chuck roast, though chuck often provides shoppers with a more affordable purchase. 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. If using an electric smoker, fill the water bowl half way and place wood chips in the tray. 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. Rump roast, like chuck roast, is a very heavily exercised part of the cow, full of marbling and collagen. Step 2: Set up and preheat your smoker to 250°F.