Put on eye protection and a dust mask. Cut the fragrant sumac at the trunk with an axe or a saw. Leave about one foot of the trunk exposed from out of the ground. Cut into the trunk with an axe or saw.
Leave your eye protection and dust mask on and put on rubber gloves. Wear only rubber gloves as leather and cloth gloves will soak up the herbicide mist and get onto your skin. Spread shrub herbicide around the fragrant sumac's trunk and into cuts made in the trunk with a sprayer. Let the herbicide soak in according to the manufacturer's instructions.
Cover the fragrant sumac's trunk in burlap or a tarp. Wrap a rope around the trunk to secure the burlap or tarp. This will rob the fragrant sumac of sunlight and rain water. Leave the trunk cover on for at least three to four weeks to kill the trunk and roots.
Remove the burlap or tarp after the fragrant sumac's trunk dies and uproot it with a shovel. Dig around the trunk to expose the root system. Pull the dead trunk out of the ground and backfill the hole.