Its green color comes from iron content; its name, from Spanish. Here's something I read from the Encyclopedia of Word and Phrase Origins:

"Spaniards in medieval times believed that this gem helped cure kidney ailments. They called it piedra de ifada, "stone of the side," which became shortened and corrupted in English to jade. The jade of old horse or a worthless woman, and the adjective jaded derive from another unknown word, of Middle English origin."

Now that's something to chew on. That unknown derivation. I suppose we know that word was Middle English because it must be found in Middle English writings, but we haven't been able to determine from whence it came. It simply erupted into usage.