I am still getting used to DF2k10, and i just got my first moody dwarf. He claimed a metalsmith's, and is, among other things, asking for cut gems. I have plenty of rough ones lying around (even star rubies), so i made a jeweler's workshop, and put a dwarf on cutting. The problem is that even though i have a gem stockpile 3 squares away, he cancels all jobs because he claims there are no gems. Help!
Like Sphalerite said, make sure that he can access the gems; a jeweler's workshop has an entire side that a dwarf can't move through. If they're in a side tunnel or room to the right of the jewelery, then they're not accessible.
If that's not it, then the most likely reason is that the gems are either forbidden or he's been assigned to cut gems you don't have somehow. You're assigning them through the workshop and not the manager, correct?
Also, a secondary question: Why are all my miners drowsy, thirsty and slow as hell even though they are legendary?
Dwarves will keep working as long as their mental attributes and endurance will allow them to do so; some dwarves will even work themselves to death if they have indefatigable and high concentration. The best thing to do is to turn off mining for a minute; after they mine the next tile, they'll go off and drink, eat, and sleep. As soon as they head for the drink stockpile, turn it back on so that they'll get back to work after they get done.
Far as being slow goes, how much booze do you have? If dwarves have to drink water instead of some form of liquor, they begin to work more slowly because of their dependence on alcohol. Does it say anything along the lines of "and can't remember the last time he had any" on their thought screens? If so, that's your problem. If not, well, their agility is lousy and that's that.