>> You can then compose your object layers seperately.
>
> Sorry, I didn't get your idea.

If the objects are separate you could render them separately,
but I now see from your example that they aren't really
separate.  With the overlapping rings which image would
be on top?  The way that you envision it either of the rings
might be.  In order to cut up your object you will need to
resort to further CSG or use clipped_by.
Example of cutting by depth...

difference {
   union {
      torus {0.5,0.1
         rotate <75,0,0>
         translate <-0.3,0,0>
         texture {pigment {Red}}
         interior_texture{pigment {Clear}}
      }
   torus {0.5,0.1
      rotate <-75,0,0>
      translate <0.3,0,0>
      texture {pigment {Blue}}
      interior_texture{pigment {Clear}}
   }
}
plane {z,-0.08 pigment {Clear} } // show rear part
//plane {z,-0.08 inverse pigment {Clear} } // show front part
}

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