Both sentences are perfectly fine grammatically. There's a small functional problem with the first sentence though: since an elephant is also a thing that is not an organic or metallic material, that would implicate that elephants are ceramics. So it might be better to shorten this: "Ceramics can be defined as materials that are neither organic nor metallic."
In the second sentence, "they" indeed refers to the ceramics, but the whole sentence is passive: the ceramics are not producing anything, instead they are being produced by some unnamed agent. It's this agent who is using clays and other minerals, not the ceramics. However, this "using" is not put in the passive, similar to Japanese (ceramicsはclaysを使って生産されます). Therefore this sentence is completely valid.