Will it start right back up? Maybe a clogged fuel filter. Not letting enough fuel to enter, but "catches" up when the engine is off.
You may try taking off your carb or carbs and cleaning it with a good carb cleaner and blowing all the holes out with an air hose.
My mower did the exact same thing and that's all it was, just one of the holes was plugs up. I couldn't see anything plugging it, but after a good cleaning it was fine.