A process is described whereby gadolinium and gallium containing by-products can be reprocessed to yield the oxides of these elements in sufficient purity to be re-used in the process for manufacturing Gd.sub.3 Ga.sub.5 O.sub.12 (GGG) single crystal boules thereby improving the economics of production of GGG wafers significantly. The gadolinium and gallium oxides are recovered and separated from transition metal impurities introduced during fabrication of GGG wafers by precipitating the gadolinium as oxalate which is thereafter pyrolyzed to gadolinium oxide and eluting the gallium containing filtrate over an ion exchange resin and precipitating therefrom as an oxalate the gallium present. The gallium precipitate is also pyrolyzed to the gallium oxide. The process can be extended to include purification and re-use of by-products generated in other grinding and polishing operations which may result in the recycling of the order of 80% of the generated by-products.