A lot of people have complained about the stone clutter, and a lot of alternatives to handling it have been put forward. I thought I'd add my suggestion to the heap:
Differentiate between mine and dig.
They would essentially do the same thing - designate an area and a dwarf with a pickaxe removes the material there. The difference is in how it's done.
With digging, the dwarf simply removes the material, leaving behind bits of material that are small enough to be abstracted away by the game, which is what I presume happens already in those cases when nothing is left behind from digging.
With mining, the dwarf proceeds more carefully, working to ensure that the excavated material is still useful for further processing. That is, essentially the same thing they do with digging now.
There's nothing to say digging would be faster than mining, it's all a matter of taste really.
Since the game already knows the difference between economic and noneconomic rock and ore, and there already is code in place to cancel a dig under certain circumstances, it'd be quite possible to cancel a dig job when the dwarf reaches something you'd probably like to mine instead.
This could be put into the interface in a lot of ways, perhaps a separate designation, perhaps a toggle after you select digging, perhaps something in the options, whichever feels best. I personally like the idea of a toggle.