Yes—cutting a gray card into smaller pieces should be fine as long as the card surface itself remains clean, flat, and neutral.

For photographic use, the important thing is that the gray area is large enough to be clearly visible in the reference shot or to fill enough of the frame for custom white balance/exposure measurement. A smaller card simply means you may need to hold it closer or frame it more tightly when making the reference image.

Based on the community experience here, even quite small pieces can still be useful. Your proposed sizes should remain practical if they are easy to photograph clearly.

There’s no strong reason to think cutting it will inherently ruin its properties. If you do cut it, make clean cuts and keep the pieces protected from dirt, scratches, and bending, since contamination matters more than the fact that it was cut.