In the Dune series by Frank Herbert, I remember reading a part where
there is advice given about fighting that instructs the listener to
"cut" and that the cut is repeatedly emphasized.  I want to know the
exact location of the passage about "the cut."

Is this quote part of the instructions?

"The good knife fighter thinks on point and blade and shearing-guard
simultaneously. The point can also cut; the
                  blade can also stab; the shearing guard can also
trap your opponent's blade."

                  "When your oponent fears you, then's the moment when
you give the fear its own rein, give it the time to work on
                  him. Let it become terror. The terrified man fights himself." 

                  "Keep the mind on the knife and not on the hand that
holds it. The knife is more dangerous than the hand and the
                  knife can be in either hand." 

                  "Killing with the point lacks artistry, but don't
let that hold your hand when the opening presents itself."

http://www.geocities.com/aeusoes1/dune34.html

This website has the entire DUNE novel (Is that legal?), this excerpt
is from chapter 34.

Bowler-g

This is the entire novel:

http://www.geocities.com/aeusoes1/dunecontents.html

Hi !

I've also searched the book on the site bowler-ga  found, and the
passage you describe is not there - the closest is the one Bowler
found.

Are you sure the passage is not in one of the sequels and related books?

I did a quick search through the original Dune series in e-book form
(all 6 books).
I searched for each of the words "cut", "knife" and "fighting" but I
did not find any other passage that fits your description than the one
found by bowler.
Do you remember anything else about that passage?