Just thought I'd mention a couple of things I find helpful when cutting with intricate dies like the Anja's Squares shown in my earlier post.
If you find that your diecut isn't easily removed from the die, try rubbing the metal die prior to use with a tumble dryer sheet. This seems to coat the die with an invisible surface that stops the card sticking. Repeat the process after a couple of cuts.
After using the tumble dryer sheet on the metal die, if you still struggle to remove the diecut and usually end up picking it out with a pin or pricking tool, try instead a ball of blu-tac just pressed onto the diecut. I usually find this dislodges the card easily and I don't end up tearing them as often.
If you find that the design doesn't cut completely on the first pass of the cuttlebug, being careful not to move the cut inside the die, rotate the die 90 degrees on the cutting plate and run it back through. Often the failure to cut the design completely is caused by the bend in the cutting plates. Rotating the die and passing it through the cutter a second time usually eliminates this.
Hope you found the above helpful.