Likewise with Darryl - I tried some epoxy resin turnings once (and a freebie acrylic blank I got from somewhere) and just from those 2 experiences with the shavings along were enough to turn me off permanently from doing any turnings with Resins.
Because much of my waste/shavings goes to my Brother (their chickens love it for dust bathing) I try to keep my wood shavings clean (as opposed to stuff with dust/dirt/debris, etc swept off the floor - Those will go into the dump trailer which carts yard waste and other stuff to the burn pile out back...
If you are in a rural enough area with suitable farmland or some such where you could have a brush pile (from land clearing or whatever) that you can burn (have to check with local fire dept to be sure you don't try burning during wildfire season or some such) It could go into such a pile, otherwise your only choice pretty much is bag & haul to local landfill -
So in a nutshell, I will not be one of those turners that does Epoxy or Resin art work. Aside from that, the stringy clingy mess of shavings that gets everywhere (I still find stray shavings now and then from 2 years ago from that resin project) are the other primary reason I hate turning resin/epoxy/acrylics - To say nothing of the ramifications of the dust/air quality issues you may see if you do enough of that work.
Upshot is- I have no real suggestions what to do with the mess, so I'd have to guess it gets bagged for landfill waste (And I have to wonder if it eventually will not become another "HazMat Residue" that gets banned from landfills requiring very expensive environmental disposal procedures.)