The Guide

Step 1: Dig out a trench

 
You’ll want to start by digging out a trench surrounding the copper vein. I found this easier by first digging a hole to “bedrock” (i.e.until you can’t dig lower), then digging at the base of the stone going around the copper. 
 

Step 2: Mine the copper at the bottom

 
This next part is straightforward – just dig the copper at the base of the vein. You’ll find the terrain extends through the vein, so you’ll need to dig this too. I’ve found that if I align myself parallel to the terrain, aim at the ground and then swing my pickaxe, it should mine out the terrain next to you. 
 

Step 3: Chip away until it drops

 
Once the vein is floating/ you’ve removed all the copper and stone below, start digging away at the edges of the floating copper. Once all the “grounded” copper is removed, all the remaining copper should break into drops for you to pick up. This is a little bit of trial and error as to which is supporting the vein, but the point is you don’t have to mine it all if you’ve done it correctly! 
 

Step 4: ?????

 
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Step 5: Profit

 
Collect your drops. 
 

Other Strategies

 
Another strategy is to use a troll to break the copper. Personally, I find this too tedious as it requires a lot of patience, both in getting the troll to swing in the right direction and how many swings it takes to break a single piece. 
 

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