You don't "get rid" of mushrooms.
Fungi, the ones that produce spore bodies, better known as mushrooms, are 99.9% beneficial in that they (1) decompose dead vegetation and make the nutrients available to plants and (2) form mycorrhizal associations with plant
roots that are symbiotic: good for the mushroom and good for the plant. When you build a
hugelkultur, or mulch, or
compost, you are adding material that will cause the fungi present in the soil to proliferate.
There is a way to "get rid" of mushrooms. Plow the soil repeatedly on hot, dry sunny days. Break all the strands of hyphae and dry them out in the sun. Then hope for a long dry spell, the
dryer, the better. If you keep at it, making sure that any vegetation dies to crisp and blows away, soon there will be no organic matter for the fungi to decompose. Then you can be rid of mushrooms and your place will look like this: