I've seen the term "Braising Steak" on packaged supermarket meat before in the U.K, but not in the U.S. It's always a tough cut of meat such as chuck, flank, skirt, etc and the name itself should be an indication of how to best prepare it, in a braise. Sear the meat well then put it in a heavy lidded container such as a Dutch oven, add some liquid (water, stock, beer, wine, etc.), a mirepoix of minced onion, carrots, celery, garlic, your favorite herbs and spices, and cook it slowly at around 275F for 4-5 hours. Check the meat and if it isn't tender enough for you, then continue on until it is.
Smoking it alone for an extended period of time will result in nothing more than a cooked and finished piece of meat that's still going to be tough as well as dry. If you want to add a smoke flavor then do so for a couple hours then proceed as above with a braise.