In my ceramics class, we use iron oxide in our glazes, but a lot of it goes to waste. We have a bucket full of scrap glaze which contains quite a lot of iron oxide, but is also mixed in with silica, alumina, titanium dioxide, tin oxide, and other substances.
Is there any way to extract the iron oxide or other metal oxides from the scrap bucket?
Assuming the iron oxide is just mixed and has not been fused with the other oxides you could use a magnet to pull it from the other oxides.
If it is fused with the other oxides, you could smelt the iron out with carbon. This will also smelt out the tin, which mixes with iron quite well. If you re-oxidized the iron in a furnace with air the iron will selectively oxidize first leaving tin metal when done. This is likely an impractical and cost-inefficient procedure as iron oxide is incredibly cheap relative to the cost of separation.
I once was using a silver nitrate and had collected a small amount of silver chloride. At the time, we were operating a lab muffle furnace (for a related reason), so I decided to reduce the $\ce{AgCl2}$ to $\ce{Ag}$. I needed some graphite crucibles and it took 48 - 72 hours of high heat. I collected an amount of silver equal in mass to maybe two quarters (US coins) with a value (at the time) of around \$15 (iirc). Total cost? Oh, probably \$50 to \$100. (Graphite crucibles were consumed, my time, energy costs, and wear and tear on furnace.)
Iron oxide is a LOT less valuable than silver chloride. There is nothing you can do to make any reclamation effort cost effective when you are competing with people digging it out of the ground by the ton.
Of course, most elements can be separated from one another by classical (wet) chemistry - after all, that's how the concept of an 'element' began - elements are the irreducible components of all matter.
Iron is much more reactive than silver - if you don't believe me, go take a look at all the rust surrounding us. Rust is, after all, just one kind of iron oxide. Since it is more reactive, isolating it will be much more expensive than isolating silver. So we have a perfect storm: it's less valuable, and would cost a lot more to process. Titanium is by far more valuable, and yet they use it in paper to make it 'bright' - so generally the only reason to extract metals would be to reduce the cost of disposal. Things like lead or other toxic heavy metals might be best handled by recovery - although generally inclusion into a ceramic is one of the best long-term storage choices, so even then, it's unlikely to be useful. And none of the processes that would be effective would be efficient with the small quantities from a lab.
Just consider all of the $\ce{CO2}$ you'd need to create (either locally, or at the (gas or coal powered) power plant just to heat this scrap to reaction temperature. As I learned long ago, (much to my chagrin), in almost all cases, (small) lab wastes are cheaper to dispose of than to repurpose.
There are ways, of course. Smelting, for one (reducing the oxides in a high temperature furnace), and leaching for another (flowing a solvent through the crushed media).
Oxides and silicates are rather stable, however, and the temperatures, reagents and solvents that attack them are not tabletop-friendly. If the scrap was well-sorted, or valuable, or too toxic to dispose of, there might be some utility in treating it.
