The simple but tedious way is to dull the punch evenly by rubbing the
entire circular edge against a stone or emery paper, then delicately
remove the flat reflective edge you have created by grinding or stoning
the outer bevel until the edge is uniformly thin and virtually
invisible.  A light final stoning inside and out with a cylindrical
abrasive stick puts a strong but fine finish on the edge and doesn't
knock it too much out of flat.

My own shop method may be a bit of an overkill in the setup, but it is
the only way short of the tedious method above that I have used which
makes a level edge.

Load a spud* in the lathe which fits the inside diameter of the punch.
Make sure there is a groove turned in the spud which is at the edge
to be sharpened.  Tighten the spud and place the tail of the punch on
or against a live center. Use a tool-post grinder to sharpen the edge.
Dress with a cylindrical stone as above.

* spud -- n. 1. potato [colloquial];  2. dullard [derogatory];
  3. expanding collet which holds against the inside of a (usually)
  cylindrical part.

Karl Petersen -- Meridian, Idaho
(and is constantly reminded of it by the license plate slogan,
"Famous Potatoes")

 [ Is there also a British usage of 'spud', meaning a spade or
 [ tool for gardening or weeding?  -- Robbie