Welcome to the forum! I’ve cut card stock just fine. I believe others have cut thinner paper as well.
A few things to keep in mind:
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You need to get a mat to hold it down so the fan doesn’t blow it away. Or, use a Krylon Spray Adhesive on top of a sheet of wood.
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You will have to experiment with settings. Here is a good place to start:
Somewhat Comprehensive Testing of Settings for Cutting Paper and Cardstock
Best of luck!