A mining engineer was an engineer who specialized in the field of mining engineering; that is, the application of engineering science and technology for extracting and processing minerals from the environment.
During Miles O'Brien's rogue mission to New Sydney, he met up with the Tigans, who ran a pergium mining operation there. Upon learning that O'Brien was an engineer, Yanas Tigan told him of a problem they were having with a trans-sonic drill that no one else was capable of fixing, and that she would be grateful if he could take a look at. Janel Tigan, Yanas' son, reminded his mother that "he's not a mining engineer," but she ignored him, and O'Brien nevertheless agreed to take a look at it, stating "it'll do me good to get my hands on a problem I can solve for a change." (DS9: "Prodigal Daughter")