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I may be wrong but it seems that the Cricut machine uses pre-programmed cartridges to cut letters and images, you cannot program the machine to cut out paper model parts.

There are machines called CraftRobo and Silhouette SD that have software to to make cutting files to cut what ever shapes you want. There is also a tracing feature to be able to assign cut or score lines for paper models that were not developed with the software. The machines score by cutting part way through the cardstock where a fold is needed. They also utilize carrier sheets which are tacky so the printed paper can be shuffled back and forth in the machine while the cuts and scores are being made.