Many of the cutters in the "Value" line are capable of cutting twill, however long-term results may vary. The value cutters all have a lot more plastic components which could potentially break under the constant stress of cutting a thicker/denser material like twill. Professional series cutters on the other hand all use metal carriage arms and industrial quality components. The only units we think might be effective from the value series of equipment are the Laserpoint 3, while using a Roland 54 degree twill/flock blade. If your budget permits the purchase of a more appropriate cutter, we strongly encourage you to take a look at any of the Professional model cutters such as a Titan, GraphTec, or Roland for this type of material.