The mushroom you see is the fruit of the fungus in the soil.
They are part of the real world and a vital part of the ecostructere.
Be thankful you have them they are doing a power of good for your soil.
The beneficial affect of fungi is just short of the benefit of earthworms
Like all flowers they only appear for a short time so whip over them with the mulching mower and that will be it for a long time.
There are only 2 ways to prevent them growing.
1) did up your soil to a depth of around 30' and remove all organic matter from the soil
2) concrete your yard.