Mihawk's sword is probably diamond encrusted
Although I previously posted that Zoro pushed himself to the limit, the very truth is that Zoro let it all go. He didn't give up, but instead of trying to force his cuts into the targets, he manipulated the cutting "essence" into harmonizing with the target's essence. This allowed his swords to go through solid steel. This is a VERY Oriental concept. The "breath" he talked about is qi (in Chinese [pronounced CHEE]) or ki (in Japanese), which literally translates to breath. It is the everflowing energy of life, nature, the universe.
Hawkeyes probably manipulated the "breath" into a pressure wave that cuts any material, especially non-living matter. Obviously his stronger rivals can counter-manipulate the breath to break the pressure wave, resulting their fight into a contest of who is the better manipulator.
The concept is that in order for Zoro to cut metal, he can't rely on power, which he believed, but he had to master his sword. He had to learn to be able to control his sword to the point he could NOT cut something(recall his master with the paper and him with the leaves) before he could have the ability to cut metal.
In essense, he just had to have complete and total control of his sword's actions.
Good. At least you have the basic idea down.
Originally Posted by Shamgi