A mining company was one that conducted mining related operations on various planets, ranging from prospecting to extraction of targeted materials.
In 2265, the Galactic Mining Company operated the Delta-Vega Station, an unmanned lithium cracking station located on Delta Vega. (TOS: "Where No Man Has Gone Before")
In 2266, a small mining company operated on Rigel XII that produced high-grade lithium. (TOS: "Mudd's Women")
Sometime prior to 2268, the future Starfleet geologist, Ensign Carstairs, served aboard a Merchant Marine freighter that had once visited Alpha Carinae II and conducted a geology survey on the planet for a mining company. (TOS: "The Ultimate Computer")
A number of years prior to 2364, the planet Dytallix B was mined for the Federation by the Dytallix Mining Company. (TNG: "Conspiracy")
Around 2369, the Jupiter Mining Corporation established an office at room 02-842 on the Promenade of Starbase Deep Space 9. (Star Trek: Deep Space Nine set decoration)