How do I create circular polygon pour cutout in Cadsoft EAGLE?
You want to draw your primary copper pour on the top (or bottom) layer, and the circular cutout on the appropriate Restrict layer: tRestict (top) or bRestrict (bottom).

The copper polygon will not extend onto the restrict-layer feature.

Make sure the copper pour is a polygon, not just a "rectangle"!  The primitive rectangle and circle features are simply static shapes which do not automatically adjust to the design constraints.

Confusingly, there is also a vRestrict layer, which actually forbids vias, not copper features.