I'm assuming you are slipping your blade under the pieces to lift them and they are still sticking and distorting? If you are doing it that way and still having trouble, some thoughts:
It sounds to me like you've got very soft clay. If it's Premo, there will be firmer clay coming along and the problem you are having will virtually disappear.
You can try leaching the clay a bit to remove some of the plasticiser. That will firm it up, but also makes it a little more brittle which might not be what you want. And leaching is a pain. It works, but it is imprecise and will slow you down.
I would suggest that you get some ceramic tiles small enough to fit into your oven. Use a Sharpie to draw the grid onto your tile so you can see cutting lines. Then leave the polymer clay tiles right on the ceramic working tile for baking.
If you don't want to use a Sharpie to mark your ceramic working surface, you can place the sheet of clay on the surface and just use a ruler and needle tool or something like that to score it. Then when it comes out of the oven use your blade to cut it on the score lines while it is still hot. If it cools before you get them all cut, pop it back into the oven for a few minutes to reheat, and then continue cutting.