Here you'll fine some stone stairs that lead up to a mostly-collapsed hall. Make your way through the cramped little tunnel on the right to find a Nordic doorway with a chest holding some minor loot. Return to the top of the stone stairs and head off down the side passage, which is slightly less claustrophobic.
This pathway leads on for some distance before opening into another room of the Nordic burial mound, where cautious players can hear a series of fiery explosions as they approach. This is because of an automatic magical trap mounted to the back wall, which launches bolts of fire at you continuously- even if it can't see you. Because of this, entering the room itself is actually very unsafe- the fire obscures your vision, so even if the damage isn't a big issue it'll make your fight with the last draugr here considerably harder than it needs to be.
This draugr is a rather powerful Scourge Lord, who is in the unfortunate (for you) habit of casting a strong healing spell on himself every so often. Your best bet for this fight is to either be a heavy melee combatant and draw him off into the tunnel you arrived through, or to be a sneaky archer and use arrows to draw him away from his trap and then pelt him out of the shadows. Magicka poison is your best friend here, as it keeps him from healing off absolutely all the damage you can do- his pool is large enough that you're going to have a time of it regardless, though.
Thankfully, once the Scourge Lord is dead, his trap shuts off and doesn't pelt you with any more fireblasts. Check his table for a gem and some alchemical ingredients, then turn to the chest behind it for some valuable treasures. You can also find a couple of moonstone ore veins on the 'ground' level of the room, and the upper floor holds not only a briar heart and some hagraven feathers, but also a valuable weapon you can use, sell, or disenchant.
Head down the narrow tunnel from the room's terrace and you will find yourself again in the front of the mine where the pit broke into the burial chambers. From here, it's a hop, a skip, and a jump back out of the mine.
Perth is very glad the mine is cleared (they were waiting on a whole regiment of soldiers sent by the Jarl) and will happily get back to his mining. He will also buy moonstone ore off of you at value, not a bad thing if you haven't learned and don't intend to learn how to make Elven arms and armor.
