I see what you are saying...
The texture assigned by using cutaway_textures isn't
flagged as being a textured surface... so later it
gets re-assigned.

I usually declare my textures so I can change stuff
at one spot. Then I declare objects without textures.
Finally, I add textures with the scene.  I don't hold
to this 100% of course...

camera {location <2,5,3> look_at 0}
light_source {<4,5,2> rgb 1}

// textures
#declare TCyan = texture{pigment{rgb<0, 1, 1>}};
#declare TRed = texture{pigment{rgb<1, 0, 0>}};
#declare TThing = texture {
   object { box {<-1,-2,-1>, <1,2,2>}
      texture{TRed}
      texture{TCyan}
   }
};
// objects
#declare Thing = difference {
   box {<-2, -1, -1>, <1, 1, 1>}
   box {0, 2}
};
// scene
object {Thing texture{TThing}}

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