I regularly cut .030" styrene with my Silhouette Cameo. It doesn't cut all the way through, of course, but it does cut it well enough that you can "flex" the piece out of the larger piece. I have found it to be incredibly useful.
I have used it very successfully, but almost exclusively when I was masking channels or other indented areas. For instance, I used it to mask the channels in the warp grills on my 1:350 PL Refit Enterprise.