I think the moist grass is touching the hot parts of the mower and that is why your are seeing smoke, you can wait for sometime so that the grass will be dried, and then you can use the mower, and keep cleaning the mower after cutting, it can clog it easily.
If you clog an electric mower with too much grass it will create so much heat inside the straining electric motor that it will melt its components and burn out- and never start again.
And wet grass tends to bend over because of the weight of water on it, and the blade of lawn mower will miss it, and that is why it is recommended to wait until the water is dried out. Moisture can also rust the important parts of the mower as well. Mowing a wet lawn require more efforts and time as well,