How to cut corners of a rectangle like this?

This is what clipping masks are used for.  Use any shape you like -- super simple or complex custom shapes.  

In this example, I used a puzzle piece from the Custom Shape library with a solid fill and border.  Notice the Layers panel.

Create a square document.

Fill the background with black

Create a new layer and fill it with white

Use Free Transform to rotate the white layer 45°