Copper is a great mirror for IR, so in addition to not having enough energy to cut the copper, it will reflect the beam back up into the laser head and probably damage it. You might be OK masking it, but you still can’t cut it.
As another caution, be extremely careful of anything that creates ‘dust’, such as polishing, burnishing, grinding, or cutting copper.
When we prepared copper bus bars for sub stations we worked in hazmat hoods with specific filters. You do not want to breath airborne heavy metal dust.
I had a friend that for most of his life made copper sculptures with a torch and phoscopper brazing rod. Naturally concerned about that issue, He did a lot of research and it turns out that while not a critical as iron, there is a minimum need for copper and it is not a heavy metal poison.
I have not worked it in many years (though I still have two rolls of it) But I see Jim Lewk is still at it at the same house where I last saw him ( It was originally built by Batista to house a girlfriend and has many quirks as a result),
Intensely working for 50 years and still at it I originally learned to work copper from him.