Deep Dwarves are a more unique, specialized civ. There would probably be more limited working positions, especially earlier on.
Examples from the incomplete Jobs section ("He" will be used, though "she" is also possible):
Lord of the Diggers: This is an influential position. The LotD commands the large-scale mining projects, and no new tunnels can be dug without his permission. He does not, however, deal with produced resources; his main objective is to dig the tunnels as needed. He does command a small regiment of soldiers to hold off golems and other such creatures found in the depths.
Lord of Earthwork: Lord of Earthwork is a position that basically deals with the leftovers from the Diggers. He has the minerals and ores in the stone removed and processed, and he controls any masonry projects. He also has control over excavation of secondary rooms and complexes, such as those used for housing.
Lord of the Minerals: Lord of the Minerals has control over what Earthwork leaves behind. He deals with smelting of ores, metalworking, forges, magma operations, gemcrafting, and other such arts. He also has command over the decoration and furnishing of secondary rooms and complexes.
Lord of Defenders: Lord of Defenders is a role given to one of the hardiest Deep Dwarves. When golems, demons, or other such forces are more powerful than the Diggers' forward regiment, he brings in his powerful dwarves to protect the city.
Lord of Engineers: This job is two-faceted. The Lord of Engineers deals with mechanics and research. He makes sure that any mechanical works in the city are maintained and keeps checks on the structure of the tunnels due to the ever-present risk of collapse.
Lord of the People: This job deals with everything needed to keep the people alive and happy. The Lord of the People makes sure wells connected to rivers are maintained, food is in good production, and other such necessities.
Again, these are examples and an incomplete list.