the noise of hitting rock with a pickaxe or a tree with an axe attracts all nearby mobs. Just using a pickaxe on dirt doesn't seem to cause trouble.

Tips for ming copper.

if you have the time dig a deep trench all the way around the copper deposits, since its dirt the mobs won't show up as much . And once your done with the trench the mobs can't get to you while you dig the copper deposit itself.

And for the deposit, once your deep enough in the trench dig out the bottom the copper depost. Don't worry about the top part. Once you deposit isnt' supported by anything the whole thing turns into rocks and ore drops. Just like taking out the first level of a building, everything above just turns to drops. its a lot faster than diggin the copper deposit out normally.

forgot to add, this should also work for Silver.