The Mush Room is a kind of one-way passage into the desert. The interior is only shown in a cutscene. It seems to be empty, save for a small painting and a model of the house.
Klaymen grabs the model and spins it, making the whole house twist down on its axis. Four FwaSheep are grazing under the mushroom and three run away in time, while the fourth remains there and is squished into mush.
Interior of the Mush Room
Mush Room spinning
As the mushroom spins back to its original position after Klaymen gets out, the only way Klaymen can go is through the Hammerboy's House, where a purple creature knocks him into a cavern, and exit by teleport machine.