I always dig out the entire node, even if it takes time.
Normally I dig the node free all the way around and then start from the top of the node and keep at it, till I can't pick further down.
Lastly I use the hoe to pat the ground, which can reveal a couple of small slivers.

Friend of mine don't mind to come round and give a hand with it, same as I don't mind coming to her world and help her gather resources.

Usually the end result of mining a copper node is around 100 copper ore, so yes, to me at least, it's worth digging it all out.