Several things can cause the engine to smoke. Blue or white smoke is usually caused by the engine burning oil.
Lawn mower engines run with the crankcase in a vacuum. The engine has a crankcase breather that lets the air out of the crankcase. If something on the engine is leaking oil, it will also leak air into the engine crankcase. If pressure is built inside the crankcase, the pressure will force oil past the rings and cause the engine to smoke.
If a head gasket is blown, the air drawn into the engine will cause it to smoke.
I would clean the engine and look for an oil leak before taking anything apart. Check the sealing gasket in the oil fill and dip tube cap. Look closely at the o-ring that seals around the oil fill tube.
If you don't find oil leaking remove the head and inspect the gasket for an area that might be blown. Usually it will be toward the center of the head so it it leaking into the crankcase instead of outside.
You could also have a problem with the rings or a scored cylinder wall. If you pull the head, rotate the engine so the piston goes down and inspect the cylinder wall for wear or scratches.