I read somewhere that placing waxed paper between your paper and die solves the problem - the design pops right out! So I decided to give it a try... and it works!
This is probably old news to experienced die cutters, but I was so thrilled I decided to post a video for other newbies like me :-)
(If you have problems viewing the video, you can see it on my YouTube channel at:
https://youtu.be/cdM2H1P3dzw)