Hello vosadrian,
My suggestion would be to cut it right back to the soil (this is called scalping) so that you actually see the soil. All of what you are cutting away is basically both living and some dead matter but it is only the top section that receives sunlight that has green foliage coming from it.
The quicker you can get it back to just the root system in the ground and then scarified then the quicker it will recover. Doing this process bit by bit isn't doing the grass any real favours.
Cheers,
BB.
