Kirito's "light-saber" versus bullets The first time we see a bullet hit Kirito's light-saber the bullet melts. Next episode we see this happen again although this time the sword cuts the bullet in 2 half's. How is this possible?

Episode 5



Episode 6
Lordmau5's theory is quite interesting, but it doesn't quite match the visual appearance of the sword as described in the light novel.


  I stared at it for a while, and found that the sword itself didn’t
  have any direction as the entire circular section was just like a long and
  thin cylinder.


* From Sword Art Online Volume 5 - Chapter 6, after Kirito bought the sword and activated it for a test run.

The corresponding scene in the light novel (also in Volume 5 - Chapter 6) doesn't say anything about the bullets melting:


  The enemy’s rifle’s muzzle suddenly let out an orange spark.
  
  During this time, the blade of the light saber blocked the lines of
  the first and second bullets with pinpoint accuracy.
  
  *BA-BAM!!* The surface of the light saber let out two bright
  orange sparks. The moment I noticed this, my right arm immediately
  pointed the photon sword onto the third and fourth bullet lines at a
  lightning quick speed. Then, the sound of the bullets being deflected off
  the intense energy could be heard again.
  
  [...]
  
  5...and that’s the 6th one! After deflecting all the bullets that could
  have hit me successfully, I kicked the ground hard with all I’ve got to
  cover the remaining distance between us.


The next scene (where his opponent ran out of ammo and had to change magazine) starts right after the text cited above. Therefore, the scene in episode 5 of SAO II is most likely something added in the anime to explain how the bullets are neutralized and to impress viewers, since the viewer can't see how Kirito neutralize the bullets if the scene is animated at real world speed.

The bullet being cut in half in episode 6 is actually described in Volume 5 - Chapter 7, though:


  From the Hecate’s large muzzle break came orange flames.
  On the other side, the blue white lightning cut through the dusk
  darkness.
  
  Shining like shooting stars, two small lights split to the left and
  right, flying far away.
  
  [...]
  
  It was cut apart.
  
  At the moment the bullet fell to the ground, Kirito’s lightsaber
  slashed upwards, and cut the 50-caliber bullet that was supposed to be
  a fatal hit. The two shooting stars that Sinon saw, were fragments of
  the bullet that were cut by the high concentration energy blade, and
  flew pass either side of Kirito behind him.


Note that it doesn't say anything about the bullet being cleanly split in half as shown in the anime.

I couldn't find any explanation on how the sword works in the light novel, though, and with so little information, we can only guess why the light saber would deflect bullet in one scene, and cut the bullet in half in another.