Cut Shapes works only on the first Element

Make sure you’re selecting the square second. With Cut Shapes, the second selected shape is the “Cutting Shape”. Since you want to cut your design with the square, you need to select the design first, then the square, and repeat that selection order for each piece you want to cut the design into.

The Cutting Shape also needs to be a “closed” shape, which would explain why, in this case, it’s grayed out if you selected in the incorrect order.