Aha! Me and Thunderbird+ have our first disagreement! Staghorn or Chinese Sumac is quite invasive. Mow as you'd like, but it's going to continue to spread. Actually, there's no guaranteed method of destroying the plant, but if you have the patience, select any full strength weed killer that is glyphosate based. Here in the U.S. I use Roundup. Select the largest sprouts you can find and cut them off. Using a common paint brush, paint the stumps (it's actually called the Cut stump method, unique, no?) with the Roundup. Find as many larger examples as you can. This will kill the Sumac, but it will take some time. In the mean time, use the afore mentioned mowing technique to control it's spread.
I don't entirely disagree with the venerable Thunderbird, but I really think next spring your in for disappointment by relying on mowing alone. You are aware that Sumac, Poison Ivy and Poison Oak are all related, aren't you? So be sure to use gloves and long sleeved shirts when handling the nasty weed...