If your lawnmower backfires when it is cut off you could try cutting it off at full throttle, some engines are designed to only be cut off at full throttle.
After you get done mowing you need to idle the moter down and let it run at low rpm for a couple of minutes. So the engine can cool off this should help.
You may have gotten grass in your exhaust system. You may want to take the engine apart and check for blockages in the exhaust. The exhaust system is a little smaller on lawnmowers that it is on cars. Also check to make sure you have the oil to gas ratio in a 2 stroke engine.