Is it a close-up of individual hairs?
Or is it a huge field of dense beard-like fur?

If it is a close-up of a small handful of individual hairs like in a tv spot, I would make the hairs out of polys and convert them to nCloth.

Then, select the vertices of the hair geometry close to the area you want the cut to happen, then apply the nCloth "tearable-surface" nConstraint to them.

Now just animate the "Glue Strength Scale" attribute of the nConstraint as your razor geometry passes over the hair to make it look like you shaved-off the hair

(see attached image)