As mentioned above digging around the copper deposit first helps a lot.
Another thing is that they won't spawn in line of sight. So clearing out the trees and brush for a ways should also help reduce spawns. Use that wood to put out workbenches that will stop spawning. Then if you have wood to spare put up a log fence.

Since greylings are afraid of fire, place a campfire nearby and you are good to dig. And dig deep. A workbench prevents them from respawn, so just place on of that as well.

It also seemed to drastically reduce the level of nuisance when I destroyed the greydwarf nests in the area. I still get the occasional day when the world seems to be carpeted with dwarves but it's no longer so continuous.

Its kind of funny. If you want rocks or wood or both to build, you can cut one tree or bash one rock and then get 3X the materials from the wave of GD that come by to check it out. Repeat until ready to build your new project.

Thank you very much for the tips. Digging around really helps, especially if I use a torch or a campfire near the vein it seems to supress their range and aggressiveness.

They are attracted primarily by sound. So yes, that is normal xx.
But I have made the experience that it stops after a certain time and you can chop wood in rest or so.

And for copper veins I always do it so that I just dig deep, because the veins go super deep anyway and from there everything degrade. Dwarves and trolls can't jump into holes or anything at the moment. Dwarves do throw stones at you, but that never really bothered me personally.

Once you get to the point where you've tamed wolves, you can take a few with you. Just be prepared that they like to multiply like rabbits, because you can also find wild boars and deer everywhere that they will kill ... so I personally would do without.

And for the roaming. You can't do anything about it. That is their territory. Kill them or ignore them.