Before a Dungeon can be Mined remotely, it must be Surveyed. It is also recommended that you Survey a Dungeon before Occupying it, although it is not required.

You will find it advantageous to scout the Mountains in the area surrounding your Mountain. You will likely find that some Resources are not available, or are expensive, in the Regional Market. You can later send out Mining crews to collect Resources from these surrounding Dungeons, although slowly. If a player later Occupies that Dungeon, you will still be able to see what Resources were available in that Dungeon.

To survey a Dungeon, go to the Overworld, pick a Mountain and click the magnifying glass icon on the bottom right to view it. Then Select an unoccupied Dungeon. Select the Survey option from the menu on the left hand side.

Your Goblins will now go forth and Survey the empty Dungeon. After Surveying, you will be able to view which Resource Nodes are available in that Dungeon, and the options to Mine it become available.