The oldest Mine I know of and at least the oldest (known) salt mine in the world is the Hallstatt mine.

Part of the Hallstatt culture which takes it´s name from the site, from carbon dating of found mining tools the mine was in operation at least from 4500 BC predating even the Hallstadt culture which it gave it´s name to.

Barth, Fritz Eckart, Heinz Felber, and Othmar Schauberger. Radiokohlenstoffdatierung der prähistorischen Baue in den Salzbergwerken Hallstatt und Dürrnberg-Hallein. 1975.

(Radiocarbon dating of prehistoric construction in the Satmines of Hallstatt und Dürrnberg-Hallein)

http://news.bbc.co.uk/dna/place-lancashire/plain/A61943493

That being said surface mining is most likely a lot older than that, but difficult to detect and/or date. Salt mines offer the dry enviroment that preserves artifacts and bodies very well.

When studying archeology I prepared a presentation about flint mining. There are very old flint mines, some are supposed to be even paleolithic.

A famous neolithic example (3000BC) is the flint mine of Rijckholt in Netherlands, where 20000 tons of flint are estimated to have been mined.