You can't kill them, pull them off if you want to, they'll disappear on their own anyway. They're just the fruiting bodies of an underground mycelium system. From the photograph, looks like a lump in the grass behind the toadstools, if that's the woody base or stump of something, that'll be why you've got toadstools.

Improving the drainage with gypsum, and the complexity of the soil ecology with compost tea often reduces them, but I don't know of anything that eliminates them.