Nope. I've done a search of the whole thing (The Lord of the Rings, I mean) and couldn't find a reference to Mines outside of those used by Dwarves and Orcs.
It just seems likely to me that they probably did have their own mines. Professor Tolkien just doesn't seem to often describe such industrial business when it comes to Elves, even though there were surely Elf-miners and Elf-farmers and Elves who did all sorts of fairly menial manual labour to keep Elven society running; perhaps they just did it so well (as you might imagine they would) that it just wasn't worth mentioning!
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"Since the evening of that day we have journeyed from the shadow of Tol Brandir."
"On foot?" cried Éomer.
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