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I cut stencils from time to time out of used carrier sheet and have found that applying a couple layers of transfer paper to the back side to act as a cutting mat works pretty good.

APPLICATION INSTRUCTIONS FOR DECAL 1. Clean window or desired smooth surface to remove dirt, grime... (70% ISOPROPYL ALCOHOL) Do not use Windex or other similar ammonia-based product, as it leaves a trace behind that is not suitable for decal applications 2. Remove and discard decal backing material (white paper) ---- peel away carefully, making sure the decal stays on the clear "transfer tape" 3. With the backing paper completely removed from the decal & transfer tape, gently place the decal with the sticky transfer tape onto the surface of the glass (or other desired smooth substrate) in the position you want the decal to be and rub it down lightly with your hand --- be careful, once it's down, it's down ! 4. Take a credit card and firmly wipe over the surface of the transfer tape to affix the decal onto the glass or substrate. The decal adhesive is activated by strong pressure. 5. Finally, peel away the transfer tape gently, at a 45-degree angle. The decal will adhere to the surface, but make sure that the decal remains stuck onto the glass and doesn't come back up ---- sometimes you have to 'coax' it from letting go of the transfer tape. 6. Your decal installation is complete. If there are bubbles present under the decal that cannot be removed by working them to the edge, a small needle or pin can be used to puncture the bubble and remove the trapped air

If I am cutting stencils I include a box around the design at the outer limits so I get the right amount of clearance around the edges. Works every time without having to remember anything fancy. Especially nice when you do another one a year later.

These cutters are not designed to cut through material, they need something on the back side to support the material being cut, ie vinyl. They make cutting mats that you can stick your material to so that the cutter can cut all they way through yet still have a "backing" that holds everything in place. Why are you cutting through the vinyl and backing?