I recently bought a very nice doily die from Lifestyle Crafts at Michaels but it did not want to cut in my cuttlebug. I had to really shim it up so that it was almost impossible to crank. And it cut thin paper better than cardstock.
I finally came to the realization that the ejection foam in the die was probably interfering with the ability to cut well. Unlike other wafer dies, these dies are entirely closed so there's no open space or holes to poke out your cuts and the bits and pieces. That's what the foam is for - to push the paper back out after it cuts it.
So I removed the foam from the outside of the cut and from the die cut shape. I left the foam in all the little places that would be the open areas in the die cut shape. I did NOT want to try and pick all those out of the die after!
You will likely have adhesive residue left behind in spots. You'll need to go back and clean that off. Or if you're lazy like me, rub cornstarch all over it and then use and old toothbrush to brush the excess cornstarch away. Worked pretty good for me - yours will depend on how much sticky got left behind.
Then I found that trying to pick the diecut out with a needle and not tearing it could get tricky (and a hassle). So I went back and grabbed a scrap of the foam, stuck it down in one little spot on the edge of the doily, and ran it through the machine to cut the foam inside the edge of the die shape. Throw away the excess and you will have this. A little spot where the edge will pop back up so you can grab it and peel out your diecut!