Can a Wood Burning Stove use a stovepipe made of copper for a chimney?

Flue fires and the lack of structural integrity of copper under this kind of heat point to no.

A custom job where you have steel stovepipe copper plated will be your solution, copper discolors under heat and picks up fingerprints so those conditions will need to be assessed.

You need to use a listed insulating stovepipe anytime combustible construction is penetrated. These pipes are also listed to be enclosed by construction. Thus it seems acceptable to me to install the listed stovepipe and enclose it inside a decorative copper tube.

For good measure, you should probably have some provision for venting the resulting annular space at the top and bottom of the copper tube.

I'm about to do this on my bus stove pipe. Copper is an excellent heat transfer material. It does become annealed at around 800 °F. However, this is far from the standard stove pipe temperature. Don't let people ruin your vision of what is safe and what isn't. Building codes are written to protect people from themselves and shady contractors, and to generate targeted business for certain manufacturers.

Follow the basic protocols for installing stove pipes: pitch, 90 bends, clearance from combustibles and proceed with caution.

Be ready to do maintenance to keep it looking bright and shiny if that's what you want. Personally I want the patina!