A properly operating and properly running lawn mower engine should not be blowing any type of smoke out the exhaust.
But when a lawn mowers engine is blowing out black smoke from the exhaust it means that the engine is running to rich and getting either too much fuel or not enough airflow.
It could be that the engine is flooding out because the needle in the carburetor is stuck open and not shutting the gas flow off so it gets too much fuel and then starts smoking.
Or your carburetor settings could be set incorrectly or need setting properly.
Also check the air filter to be sure it's clean and not restricting airflow to the engines carburetor.
The problem causing the lawn mower to blow black smoke could be a faulty carburetor, incorrect carburetor setting, choke could be on or choke could be sticking on etc.
The black smoke though is always a problem of either not enough airflow or too much fuel getting into the carburetor.