Gopro make a small mount that changes the direction 90 degrees. That'll be the easiest but will make your camera sit higher. See the piccy mate and the small one by itself would work. Otherwise take off the mount by using a sharp blade working your way around gently until you can lift it off and put on a new one.

If you want to remove the existing Gopro mount off a board its no easy thing. I put one on the nose of my original Naish Nalu and it took some pretty intensive work to get it off.
Brand new blade in industrial box cutter and lots of effort in going around and around to get underneath the mount and cut the glue (its bloody strong stuff).
Once off, the board cleaned up fine. Just take your time and watch your fingers.
The mount pictured is great for making the camera higher, it works great on windsurf booms, bike handlebars etc.