When your lawn mower is blowing blue smoke it's a sign that your lawn mowers engine is burning oil.
When a lawn mower burns oil it causes blue smoke to come out of the exhaust.
Some reasons for a lawn mower blowing blue smoke include.
Overfilling the lawn mower engine with oil.
Worn out piston rings.
Damaged or bad valve seals.
Leaking or bad head gasket.
The oil gets into the combustion chamber of the lawn mower engine when it shouldn't be and could be a sign that the engine is worn out.
A common cause of the lawn mower blowing blue smoke is due to too much oil.
Check the oil level and ensure it's full but not overfilled and if it's overfilled you should drain some oil until the oil level is at full.
If it's still blowing blue smoke then the lawn mower engine is on it's way out and continuing to use the lawn mower can result in a rod being thrown through the engine.
Of course if it's an old engine that is not worth replacing such as on a push mower then it is okay to use the lawn mower until it fully gives up.