I want to have two shapes on top of each other, simplified shown in the image below.
The design should be printed with a hot stamp method, so the manufacturer needs to have the vector graphics of each color in a separate layer. If I simply hide the black layer, the blue circle will display (and print) as a full circle. Is there a way of removing the covered part from the blue circle without having to rasterize the design?
Yes, of course. Go to Windows > Pathfinder then select both circles and click the remove-button in the Pathfinder window.
Ensure that your circles are converted to shapes! Object > Expand