shinogi wo kezuru
I have to credit this phrase to the same guy who taught me 四面楚歌, as he was a treasure trove of battle-related expressions. The understanding of this expressions relies on some understanding of katana anatomy, so we'll get that out of the way first.
鎬（しのぎ） in this phrase refers to the most prominent part of the blade, the part tucked between the actual cutting edge and the rear of the blade. The shinogi can either be close to the back of the blade, thus making the cutting edge longer and sharper but more fragile, or closer to the edge of the blade, making for a sturdier build with an arguably duller cut. Now that you are learned about the placement of the shinogi, and also that it is separated from the edge by a sharped portion of steel, we can get to the definition.
1. A swordfight so epic that the combatants are chipping away parts of each other's swords.
2. A fierce competition.
So the expression breaks down to "chipping your shinogi", or "shaving away parts of the edge of your sword". It's important to note the implication that the two opponents are evenly matched. If one side slaughters the other, it can't be said that they 鎬を削る, since breaking off pieces of your sword on somebody's skull doesn't constitute the same challenge. Unless you're fighting Wolverine. Or the terminator.
Wolverine versus Terminator... Now THERE'S a battle I wanna see! Those two would definitely have some epic clashes!