So if an object is behind another one, it is cropped so the hidden part is removed.
For example the red rectangle has been cropped as I wish in this image: 
Ideally I would like to do this for all objects in the document.
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1Why do you want to remove, by doing so you just adding more points increasing the file size.– Botond VajnaCommented Nov 1, 2020 at 6:50
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1Also you will cause renderers to show conflation artifacts.– joojaaCommented Nov 1, 2020 at 7:33
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Hi. Welcome to GDSE. I agree with the other commenters here, this doesn't sound like a good idea for both reasons already given. Why do you want to do this? What are you going to use the graphic for? Is there some specific reason that you forgot to mention?– Billy KerrCommented Nov 1, 2020 at 10:50
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1 Answer
Before you do this, please consider carefully why you need to do it. Usually this is not required and can cause problems with vector graphics - it can increase file sizes unnecessarily, and it can also cause conflation artefacts where the shapes butt up against each other, as others have mentioned in the comments.
If you still want to do it, try this:
Move one filled shape over another. Copy the top shape.
Select both shapes and do Path > Difference - the top shape will punch out the shape below it.
Do Edit > Paste in Place to paste back the top shape which was consumed in the Difference operation.
Example
answered Nov 1, 2020 at 19:56
