What the above poster was trying to explain is that on certain mopeds, the ignition coil's "earth" side passes through the brake bulb in your taillight, so when the brake is applied, it will kill the bike.
In this case, that's not the problem because last time I checked the Puch's ignition coil doesn't utilize the brake light in this function, and also because just setting the rear wheel to earth while running wouldn't even utilize the brake light anyway.
Most likely, I am going to lean towards a stuck clutch. You can pull the cover and service fairly simply. If you haven't changed the fluids/inspected the trans since buying, now is the time.