Most commercially available laser cutters, and some homemade ones, work in the 20-100 Watt ranges, using a CO2 laser. They have more than enough power to cut right through a lot of materials so ...
If you want to skip the materials discussion and watch the job, laying the fabric in the machine starts around [3:16] in the video. [fiercekittenz] acknowledges that her large 100-watt CO2 laser ...