That's up to the DM....... You can't normally use Craft skills to increase the value of an item, just to create new items with raw materials. Normally you'd use Craft (Gemcutting) to fashion a piece of jewelry or other artistic/decorative piece from gemstones.
But it makes sense that you could probably use the skill to turn a rough or uncut gem into a finely-cut and polished gemstone that would be more valuable than the raw material. So if you found a rough gemstone or crystal you could probably turn it into a more-valuable piece with enough time and work and successful Craft (Gemcutting) checks. But once a gem has already been cut, further work on it would probably just ruin it or whittle it down to a less-valuable or equivalent-value form. Maybe it could be slightly improved, but the difficulty of the task would probably be higher.
Mind you, when you fail a Craft check, you typically ruin or waste some of the raw materials. So if you're working on a gemstone, any failed Craft check will automatically reduce the gem's value, permanently. Like cracking an amethyst in two, or shattering one side of it, or whatever. You could still attempt further Craft checks to fix what remains of the gem, trying to carve it into a valuable-looking piece, but the new value will be based on how much useable raw material you had left after the mistake, not the original value of the undamaged original stone.
Cutting a gemstone of average hardness would probably be DC 15, while one of high hardness would probably be DC 20, while fixing/improving a poorly-cut or damaged gem would probably add +5 or +10 to the DC. Cutting a relatively-soft or flaky stone would probably be DC 5 or 10 depending on specifics. Of course, the DC would also be higher if you were trying to make a perfect-cut stone for maximum value (such as taking a large, rough, blue-white diamond and trying to cut it carefully into an 8,000-GP sparkling, brilliant, perfectly-cut diamond; that would probably be a DC 30, DC 35, or DC 40 task).
