To harvest copper you'll need a rare (blue) pickaxe, which you can craft at a crafting bench with three sand claws from desert beasts, and three flexwood rods, made from the flexwood that comes ...

These don’t yield copper as far as I can tell, but you will need brightcore to make copper bars. Equip your Rare Pickaxe, and harvest some brightcore before continuing your search for copper.

You can see what copper rocks look like in the image above. To mine it, you will need a good pickaxe, meaning rare (blue) quality and above. Otherwise, your pick will simply bounce off.

Again, whip out your Pickaxe and begin chipping away at the Copper Ore to add it to your inventory. Now you’ve got all the required resources, you need to take them to a Metal Smelter.