Thank you Todd... That makes sense.... I'll try a thicker paper

)) Thanks for your help...
Gigi also responded to my email I sent her... She said:
"As for construction paper, we never recommend cutting construction paper. It is one of the hardest papers to cut, especially in detail. It is made for scissors – not an electronic machine. You would get much better results using a higher quality textweight paper (will keep costs down rather than card stock) and there are some great quality and weighted text papers out there – also good lighter weight cardstocks.