Thank you for your interest in our laser cutting. We have tried cutting Tyvek before, and the results were OK. Here are some issues to be aware of:
With paper-like material, the edges of the parts will probably get burned or charred. Also, the cuts might be less precise than when cutting a rigid sheet of material since the material will not stay as flat and might flutter around a bit from the exhaust during cutting.
Note that stacking sheets sounds like a good idea but causes problems and requires a lot of testing that might not be worth the cost depending on the final number of sheets you plan to cut.
Some problems with un-masked, light-colored material such as Tyvek include higher visibility of burn marks on the back side of the material (from the laser bouncing off of the cutting bed back onto the sheet), and residue from previously cut materials on the cutting bed leaving marks on the back side of the material.
Other general issues to consider are at pololu.com/docs/0J24/4
We would highly recommend doing a smaller test run before placing a larger order to see if what we can do will suffice, especially if you need Tyvek parts with a lot of small details that are precisely aligned, or if how the final piece looks (not just the shape of it) matters a lot.
If you are interested in having us laser cut your Tyvek parts, please give us a call to discuss your requirements. I hope this helps!