Comment 1 for bug 171091

This is unlikely to be implemented in the way you describe.

I can't simulate it using the 'Cut Paths operation either!
(Cut paths seems to lop off rather than divide, this is
arguably surprising behaviour and therefore a bug).

If you really need this in Inkscape, I suggest that you:

1) Organise the requests so that there is one per entry in
the tracker.

2) Devise a UI for your 'Carving Knife' or 'Chain Saw' tool:
Possibly harder than you might think ...

I can't see this being made a priority item, but you never know.

In the mean time, you might find that in degenerate cases
such as a vertical or horizontal line, you might be able to
run a perl script on the XML.

Alternatively, one of the Power Geometry technologies,
videlicet,
http://www.maa.org/editorial/mathgames/mathgames_08_01_05.html
might be of help.