I use my Cricut cutting machine primarily for cutting puppet parts. It does a great job on making clean, symmetrical forms out of felt. Here is a small demo of the machine printing several tongues.
I design the shapes in Adobe Illustrator and then export the files as SVG. The SVG format imports into the Cricut Design Space effortlessly. I use this machine to cut almost all my felt shapes including eyelashes, mouth plates, and even the felt circle for the base oh my handmade stands.