How To Get Coins Off Plastic Cube?

Use a band saw to remove as much of the excess plastic as possible. Immerse in liquid nitrogen. The extreme cold of the nitrogen will make the plastic extremely brittle and the very different expansion rates of the two materials will cause the plastic to pop loose from the surface of the coin. Remove the coin plastic lump from the nitrogen and hit with hard plastic mallet or a a hammer through a wood block. The brittle plastic will shatter and come away from the coin. It can be done, but in most cases it isn't worth the time, effort, or expense. By the way if you do this be very careful handling the nitrogen. If you don't know what you are doing, it can be very dangerous.

I too found that out attempting to free coins from slabs. Using a Dremel or Saber saw with a metal cutting blade is almost fun. As fast as you can move, the blade starts to get hot and remelts the plastic right back to where it was.
A harsh toothed blade for rough cutting wood usually shatters the plastic.
Going to any shool and asking if you could use some liquid Nitrogen might be fun watching them call the police. Going to any school and asking to use their chem lab is something I'd like to watch with all the things happening with chemicals.
Back to that coin in plastic. One sure method would be a Butane Torch. Yes it will possibly melt all the plastic, create plumes of deadly gasses, damage the surface of the coin. BUT it will be out of that plastic. MAYBE.

Maybe buy a few 5 packs of cheap saw-zall blades made for wood cutting. Lock it in a vice and put it some time cutting through it slowly. Or if just a hammer didn't work, maybe a hammer and chisel? Whatever you do make sure you wear eye protection, it would not be fun to take a 1/4" piece of plastic to the eye ball!!

PMMA Poly(methyl methacrylate) which is typically used to make these cube,can be removed with any of the following....acetone, benzene, chloroform, MEK, THF.

But without access to a lab you won't be using most of those

And with enough money an entire company could be hired to remove those coins from the plastic. Why spend a few thousand dollars attempting to use all sorts of chemicals and/or Nitrogen when you could simply hire an entire organization like DuPont, for example, to do this. What is a few million dollars to free those coins?

I spent a couple years getting a 1967 SMS set out of a block of plastic ..
My mother had bought it at a yard sale for 50 cents.

I tried the hammer .. and the saw .. took a lot of effort but got a couple out.

The last couple coins came out best by taking my drill press and making holes all around the coins then putting them in my vice and hitting with a 2 pound hammer

Old topic... but would be a good science project to find the best way to remove coins from the clear plastic substance. I'd take a 30lb sledge to it first, probably try a variety of chemicals too.