Why does your lawnmower shut off when you push it to go over the grass Stays on as long as sitting still?

When the blades start to cut the grass, more load is applied to the engine and the governor activates the throttle to compensate for the extra load. First of all, ensure that the fuel filter is not clogged and thereby not supplying the necessary gas. You might also check the air filter which if very dirty will cause the engine to flood and die. If filters are okay, check for disconnected or broken governor spring.