Gouge mining was a type of mining practiced by the Ferengi.
In 2369, Nava came to his Grand Nagus, Quark, to complain that he felt that he had done all he could in the field of gouge mining, and that he longed for a chance to find profit elsewhere. (DS9: "The Nagus")
It is possible that the material that Nava mined through gouging was arcybite, given his interest in arcybite refineries.
A cut scene from "Ferengi Love Songs" mentioned gouge mining on Feckle Prime. Zek complained that last year that would have been a good idea, but presently he was not sure how much more gouging the planet could take. (Star Trek: Deep Space Nine Companion - A Series Guide and Script Library)
Gouge mining was also mentioned in Legends of the Ferengi, where it was said that there were gouge mines on Ferenginar, and that in the hierarchy of Ferengi jobs gouge mining was third from the bottom.