Gladi8er65's trick also works for silver nodes in the mountains as long as the sliver node remains connected to the earth. If the silver node (or the copper node) becomes "unanchored" to the earth it pops into a shower of ore and stone. You can also often find 2 or even 3 silver nodes in a single spot.
https://steamcommunity.com/sharedfiles/filedetails/?id=2856429325

@OP it takes the same number of pick swings to get copper ore as it does to get tin ore. Just throw the rock away if you don't need it. The devs did it this way because that's the way it is in nature. There is a great deal of stone mixed in with copper, silver, (and gold) deposits but mineable tin is often found in large blobs with hardly any stone intrusions.