Yes, you can cut the mushroom. You can either slice the cap off the "stem" (as short as it may be), the cap will grow a new stem, and the stem will grow a new cap. Or, you can slice the mushroom like a pie -- in half, quarters, eighths etc. You can use netting or veil material and rubber bands to hold the pieces down on rubble, or you can place the pieces into a small plastic tray on some sand. With sand, once the mushroom pieces attach to the sand, you can glue the sand to a larger base (rock...). With the netting, the mushroom should eventually affix itself to the rock.
The first cut is the hardest
Jenn