Cutting out really tiny pieces of clay can be a real turn off. They end up distorted or stuck in the cutter. If you're using plastic cutters especially, you're going to encounter a lot of problems. Also, if you're not cleaning your plastic cutters you're going to ruin them fast. It's not too hard to do and it will keep them sharper longer. Plastic cutter edges won't stay sharp even with thorough cleaning because the polymer clay eats at the edges but with proper care it's nothing a needle tool can't fix.
Do this on a sheet of paper and your clay won't stick to the table. You can peel the paper off the back like a sticker instead of trying to slide a razor under the clay.
1. Place your tiny cutter at a 90 degree angle on the clay. Push straight down. If you're cutter tilts or comes out from under you, you may be able to salvage the clay bit, but just make it easy and go slow.
2. Turn your cutter clay side up. See all that clay stuck on the edge? Push down hard with your finger to cut the edges OR (this is easier) just push the clay towards the center gently and clean it off the cut piece when it's done.
3. See how the piece goes down into the shaft of the cutter? Go with it!
4. Whack your cutter straight down onto your work surface at a 90 degree angle. A few inches off the table is a good distance, anymore and you might
hit off center and do some damage to the tiny bit. See how it is sideways in the cutter? That's good!
5. After a few good sharp taps the clay will start to work it's way down the cutter. When you can wiggle your piece to where it's poking out, start tapping the side of the cutter (with a tad less enthusiasm as before) until it falls out.
6. See how it's rugged around the edges? The back will also have a little bit of clay build up.
7. Use your needle tool to smooth the edges. Put your best looking side up of course.
8. Eeew, dirty cutter. Wipe most of the clay off with a rough towel.
9. Use a needle tool to clean the edges and scrape off dry clay.
10. Wipe with a towel again and enjoy your cutter for years. (I've had mine for several years and they are just now needing to be replaced)