A laser cutter will do a good job when cutting felt but there are significant drawbacks to that technique. Synthetic felt will form a small melted bead along the cut edge, and wool felt singes and smells like burned hair. There's also a limit to the thickness of the felt you can cut with a laser. If you have access to a waterjet cutter, it's a great alternative, and can easily cut through thick, dense felt. The finish on the cut edge is excellent.
I stacked and glued the parts I made with this technique to make a vase out of industrial felt. In this Instructable, I'll show you how I made the sliced form and used a waterjet to cut out the parts. Assembly instructions will follow in a separate Instructable.