I had some leftover stained-glass effect window vinyl from our last house. For some reason I held onto it. I decided to try gluing it onto some white vinyl tarp and see if it would take to being cut on the vinyl cutter. It did. This is essentially cutting through three layers of vinyl.
Update: well, the two layers didn't adhere well enough so I tried sandpapering the layers prior to gluing. Adhesion was still not that great. I'm not sure what to make of it.