I would like to reuse the waste material I have from trimming and grinding quartz and I had the idea of mixing the material with epoxy, shaping it, and then putting it into a rock tumbler. Will a rock tumbler smooth and polish epoxy? Has this been tried before with success, and if so is there a specific type of epoxy that is needed?
You can definitely mix the quartz waste with epoxy. In fact, it can be mostly waste, with just enough epoxy to bind it together. Mix thoroughly so all of the quartz is covered with epoxy and there aren't pockets of quartz powder. It's also helpful to press the mixture into shape to force it together and eliminate tiny gaps and air pockets (you want a solid material containing only quartz and epoxy).
If there is a lot of extremely fine quartz dust, it will act as a thickener, making the epoxy like epoxy clay that you can shape if you get the ratio right. Coarser quartz will act as a filler, saving epoxy and imparting strength and hardness. But the mixture will have a tendency to slump. If the mixture isn't like clay, you can use a mold to create and hold the shape you want until the epoxy hardens.
Rocks are very brittle and heavy, and a rock tumbler works well at knocking off sharp edges. Even the most brittle epoxy is much more resilient than stone, and lighter. If you use a brittle epoxy as a binder for a mostly quartz mix, a rock tumbler is likely to smooth edges if you run it long enough.
Polishing will be different from stone. The epoxy will already have a smooth, shiny surface. If it is clear, you will see the quartz, but the surface will be epoxy. If you haven't used a mold, the surface may be bumpy, but it will be epoxy and shiny. So polishing isn't what you need.
If the surface is bumpy or you want to expose some bare quartz, grinding or sanding is the way to do that. The fastest way to polish it is sanding with a very fine grit.
Doing this with a rock tumbler, the results will probably depend on the mix of quartz and epoxy, and the condition of the surface. If the surface is not uniform (e.g., crevices or a lot of high bumps), a rock tumbler isn't likely to be effective, at least in a reasonable time frame.
You can avoid the need for a rock tumbler by using a mold. If you are making freehand shapes, do it in a medium like clay. Polish the model, then make a mold of it. The quartz filled epoxy will come out in smooth, polished form.