Use bone cutters to cut the disc (they cut easily and split straight usually) once you split the disc under the foot with cutters use a new razor blade or scalpel cut the 2 halfs , depending on the size it can be split up like this 2 or 3 times usually but the smaller pieces tend to come loose easier.
I would invest in a mushroom box I lost a baby OG bounce 3 weeks ago because I wasn't using my mushroom box
Another easy way is to take the shroom and pull it out of the water let it close up , then glue a piece of a frag plug directly next to the foot .( I usually choose wherever it is closest to the edge of the plate)
If its touching the foot or close it will attach itself to the surface of whatever you glued down eventually.
I wait a month or 2 and when it attaches i slice it off (usually 1/4 or 1/3 of the mushroom)and pop it off the plate.
Mushrooms are pretty tough so it's hard to mess it up they are very resilient usually the worst thing that happens is they come loose and float away that's why I suggest the mushroom box. Good luck