I haven't found the time to play with it myself, but one of my team members - Mary J - blogged some tips from her experience. Just thought they might help you mgulka, since you've already shelled out on the tool!
Mary J's Hints and Tips On Using Sew-Easy Tool
Mary has managed to use it on Bazzill cardstock.
You do need to use a mat underneath, and Mary talks about this in her post - something firm yet soft, like a soft mousemat or of course the mat WRMK produce - which thinking about it, I imagine you have, mgulka, if you bought a complete kit!