Gondolin is specifically stated as having mines. Consider this statement about Maeglin:
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"he gathered about him all such as had the most bent to smithcraft and mining; and he sought in the Echoriath (which are the Encircling Mountains), and found rich lodes of ore of divers metals. Most he prized the hard iron of the mine of Anghabar in the north of the Echoriath, and thence he got a wealth of forged metal and of steel, so that the arms of the Gondolindrim were made ever stronger and more keen; and that stood them in good stead in the days to come."
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This is the only statement I can find in
The Silmarillion about Elven mines, but given that so many Elves lived underground, including Thranduil, I would consider it very unlikely that they didn't have their own mines. Mines tend to usually be mentioned in the context of Dwarves and the enemy, it seems, but I wouldn't say that means that the Men of Gondor, for instance, who were great metalworkers, didn't have mines.
Considering how much the Noldor loved working with metal, I'd say it would be practically essential that they had mines of their own. I can't see Eregion not having its own mines, for instance.
That being said, I'm sure some Elves did acquire it through trade with Dwarves; not Thranduil perhaps, but those with friendly relations presumably could have.