How hard would it be to make a laser cutter that can cut other than just straight down? IE at a 45 degree angle or other angles as well. I don't even know where to start on that sort of project.
I was thinking either with mirrors or with servos moving the laser.
Please let me know about any problems you can think of, I didn't think about as I want to learn.
you cannot create a very precise cut because of the way the laser works, however it is possible. You would have to find a way to move the laser, and write a program to move it in order to move the laser as it cuts. If you look at the picture the focal point is in one area but the whole hourglass shape is cut into the material, and as it is shifted it will cause issues with cutting. 
You're probably better off filing it down or using a router
