Q: How do you get cookie cutters like this to not stick?
A: Dip the cutter in powdered sugar and push it out with a paintbrush very carefully.
Lightly press the cutter into the dough to get the impression then hand cut the rest of the way though.
Freeze dough before cutting, dip your cutter in flour or ppwdered sugar..
These are for cutting fondant, not cookie dough.
If you have a dremel, you can sharpen that section of the plastic cutter.
Try covering the dough with plastic wrap and then cut. The edges will not be as sharp, but it releases well.