Pulling the tape against the blade won't work.  The tape is too stretchy, regardless of how sharp the blade is.  I typically do a little of both.  I do NOT cut against the surface, but rather I'm lightly pulling the tape against the blade and sliding the blade at the same time.  I new blade will cut very cleanly.  I have also taken a metal straight edge and laid it on the surface, placed the tape down and cut it on the surface of the straight edge.