A laser cutter will cut, score, or engrave a whole range of sheet goods, such as wood, paper, or plastic. Some places can even do metal.
Some props shops may be lucky to have them, or have access to them through another department. Others may have worked with local businesses for laser-cutting services. Luckily, with the internet, you can still take advantage of laser cutting if neither of these are available. There are a number of companies where you can send a CAD file or drawing, pick a material, and they will cut out your design and ship it to you.
Custom Laser Cutting is a great example of one of these companies. Their website clearly lists what materials they can and can’t cut and what is possible with laser cutting, as well as the drawbacks. With small orders, they have a turn around of 3-5 days plus shipping time; for extra money, you can get it faster, all the way up to same-day turn around and overnight shipping. They show examples of their work with prices. The black cat at the bottom of this post, which is 9″ by 11.5″, cost $41 which includes shipping. If you were to order the materials online, it would cost around $15 to have a 12″ by 12″ sheet shipped to you. If you have to pay for labor, or if you have a limited time line, this can quickly become the more economical option.
Big Blue Saw is another company set up to do fast laser cutting for small orders. Their website states they can have an item ready for shipping within 3 days. There is no information about prices, but you can request a quote.