So I spent a good part of tonight combing through the Silhouette Cameo user manual. I think I can now pretty much say it won't cut mylar stencils, but the information you need to know this is not available until you actually buy the machine. So now I feel like it's my job to make the information available for other folks considering this unit.
The user manual says, ". . . the Silhouette can cut [with] up to 230 grams force." (This manual is available with the software, so you don't have access to it until you buy the unit. I even went to the Silhouette website and searched around for different search terms to find it; I failed.)
I dug around for a while tonight for information about the force needed to cut the different thicknesses of mylar.
One material recommended for stencils is a paper-backed mylar so you can feed in the plastic without the cutting mat. There is a seller selling the stuff on eBay. Its description says, "Clear-Cut 5B™ is a 5 mil clear Mylar® polyester stencil material on a heavy kraft backing with BR-3 adhesive. . . Requires a minimal 350 grams of down force."
So, it is not surprising that my attempts only etched the mylar.
So, there you have it, the Cameo will not cut reusable stencil mylar (5 to 7 mil or thicker). It would have been great to know this before I bought it, but at least now I can provide a service and help others avoid the wasted money if what you want to do is cut reusable mylar stencils at a reasonable cost.
I guess I need to explore some of the other thinner quilting plastic options suggested. And I should still be able to use it to cut fabric. But I am now very disappointed with this purchase.