While it is very much the central tenet of all things Dwarven to be miners there are a few small clans that have taken to farming life.  Usually these clans are looked down upon with disdain for they likely lost their mines to orcish invaders (or Smaug!) in the past or, quite possibly, the mineral veins dried up.  I've sometimes used the background of searching for a new mine as an impetus for a character's adventuring abroad.

There are also tradesmen who travel abroad with the mine's wares.  After all, you simply can't trust a human to give you a fair price for your ingots and gems when you're located inside a remote mountain.  "Here's two bags of oats.  Give me a gold ingot!"

There's also a tale of one group of dwarves in southern Faerun that live in something similar to the grand canyon, only deeper, and they literally live in the walls of it.  I can't remember their names as it has been a decade but it's a very atypical twist on the common mine.