If you don't mind waiting a long time, perhaps you could use solar sails? Although, I'd guess that solar sails are only useful for providing radial acceleration (i.e. away from the sun), so this might not be useful if you're mining the stuff beyond the earth's orbit and are trying to bring it back home. And I doubt there's an analogue to "tacking" in the vacuum of space.
An alternative is to use solar cells to provide electrical power, and use the copper itself as propellant in some sort of high-efficiency ion engine or accelerator. You'd be cannibalizing your payload to use as reaction mass. Copper probably isn't an ideal propellant in such a system, but if you have billions of tons of it, you probably don't mind wasting a significant fraction of it.
A third option could be nuclear pulse propulsion. Something like the orion project?