Hey there, I am not sure if this helps you or not, BUT I was having the same problem, I couldn't even get it to cut all the way through paper, particularly the snowflakes in the center of the die. I have a Cuttlebug, too, it's a few years old.
I ran the die through twice with aluminum foil (hopefully this dies not damage it? it's a trick I've had work well for punches through the years) Then I did the following "sandwich" (I don't have a metal plate) A plate, Chipboard/cardboard (I used the back piece of cardboard off of one of my 6" paper pads), a piece of scrap cardstock, C plate, die, cardstock to cut, B plate. Once through and it did the trick. Before I removed the cut part, I rubbed my thumb over it all (particularly the areas that weren't cutting through before) and made sure I could clearly see that it had cut all the way through.
I'm thinking the heavier duty machines may work better for the more intricate dies, also my plates are really warped and chewed up from so many uses. I think it's time to invest in some new ones, but I was able to get a clean cut with that die in my Cuttlebug by using the foil and then the sandwich I described.... good luck, I hope that helps!