It would be great to have a option similar to chop down trees, but instead be a selector for dumping items. The problem is that i dont think a single tile dump square is supposed to hold a thousand dumped stones. The way its handled may change in the future since it is fairly realistic to have tons of stone needing to be dealt with when you dig a mountain fort.
A bit of a trick ive started using is designating a garbage dump, and then surrounding it with a fairly large stockpile of rock, 7x7 tile actually. A dwarf will haul to a stockpile quicker than dumping ive noticed. (It puts more items in the job queue so theres more chances of stones being moved faster seemingly.) Anyway, let the dwarves move the stone to the stockpile, and once its full, dump all of the rock in the stockpile to the garbage zone a few squares away.
This saves you from having to scroll through entire fortresses to find all that spare stone, and also puts it all in one location for easy dumping so you can just hit the arrow and then "D" which is a lot easier than having to hunt around for each stone individually.
I still make sure to dump stones that are blocking doorways or stockpiles first though, but using the stockpile method, gets rid of tons of excess stone fairly quickly, and with minimal hunting. It might actually be more work overall, but its a lot easier on the wrists, and has a positive benefit of being placed near my stone mason's shop.
I may also use it as a quick way to change the types of stone in my stockpile too. Normally set my stockpile to allow all stone, but when you want to build with a certain stone type, change the stockpile setting, dump all the stone thats in it currently, and unforbid a few pieces of the stone you want from the dump. Will then fill the mason's stockpile with the new stone type. In theroy, anyway, i havnt tested it, but it should work.