Yes it sounds like a classic case of plugged fuel filter- just like on a car it will usually start and idle fine, but once you go to accelerate in drive (as is turning on PTO clutch to mow) it loses power and dies. Then it will restart after a few minutes, but the scenario keeps repeating. Try filter and gas cap first as JTKub said, as they are cheap and easy. The fuel pumps can and do fail, but are a much less common cause of starvation. Only after checking those things would I start to fart around with the carb.
-Fordlords-