When you have blue smoke coming from your lawn mowers exhaust it means that you're burning oil which can be caused by worn piston rings, overfilling the engine oil or tipping the engine on it's side allowing engine oil to get into your carburetor.
You could have a bad crankcase breather or a crankcase air leak.
Most times the lawn mower blowing blue smoke due to burning oil is caused by tipping the lawn mower over and after it runs for awhile the blue smoke should clear up.
You should avoid tipping the lawn mower on it's side and instead just lift it upwards to avoid the engine oil getting into the carburetor and then causing the lawn mowers engine to burn the oil.
White smoke coming from a lawn mowers exhaust is also another indicator of burning oil along with the blue smoke.