Mower blows heavy blue/white smoke at random.engine stutters stops after idling a bit then does it again rounds later

Blue exhaust smoke usually suggests the engine is burning oil. Oil in the cylinders can foul the spark plugs and cause the misfire. Have you checked if the head gasket is OK? Check if there is any oil floating in the coolant bottle or any white 'cream' like liquid mixed in the oil.
If the gasket is OK your issue gets a bit more serious. You could have PCV issues worn valve stem seals, worn piston rings, and depending on the age and engine fitted you could also have a turbo oil supply issue.

The mower decides how much fuel to use depending upon rpm. When it hits a tough patch rpm goes down and the throttle opens up. In this case the throttle opens too far and the engine floods producing the white smoke. The plug is temporarily fouled out and the engine quits. After the gas evaporates the plug will operate normally again.

Sounds like a blown Head Gasket

Just letting you know that white is water, blue is oil and black is gas coming out of the exhaust.

You don't mention what that smell is reminiscent of?

You don't mention the colour of the "smoke" and you didn't say whether the engine is petrol or diesel?

You don't mention whether the road behaviour/performance is normal?

White smoke is almost always steam or in the case of a diesel it could be an unburned fuel mist, grey/black is excess fuel and blue or grey/blue is burning oil.

Some steam is fairly normal until the engine and exhaust system is hot but excessive amounts could be one symptom of head gasket trouble. If the engine is drinking coolant and sending it through the exhaust as steam it will sometimes smell spicy.

Burning oil smells a bit like burned eggs in the frying pan.

If the car hasn't ultra-low sulphur oil and fuel the catalytic converter will convert sulphur traces into hydrogen sulphide - the bad egg gas...

Does it overheat at all?

White smoke? or Dark grey smoke?

Could be Oxygen sensor (grey) or head gasket (white).

CHECK ENGINE COMPRESSION.SOUND LIKE YOU HAVE WORN ENGINE VALVES AND PISTON RINGS AND VALVE SEALS IF ENGINE SMOKING BLUE.IF YOU ARE GETTING HEAVY WHITE SMOKE.YOU HAVE A BLOWN HEAD GASKET.WHEN DOING COMPRESSION TEST IF COMPRESSION READINGS 90 - 80 WORN RINGS 60 - 40 BLOWED HEAD GASKET.

White smoke is most likely cause there is to much in the engine.. Only takes about half quart.. Clean with degreaser and garden hose on the outside..

This engine has a badly designed combustion head that causes premature failure of the head gasket. The removal of the overhead cam and head is relatively easy with the engine mounted on the mower. Just remove the hood before you begin. I had the same problem, same symptoms (white oil smoke, mostly when turning or on an inclide-=left side downhill) after the second season of mowing. Made me mad when I got it apart and saw the incredibly stupid head design. Replaced the head gasket and am into my second season with the new head gasket with no more problems but I expect it to blow again at some point. Poor engine design. Easily fixed.

look for problem injectors and leaking injector seals