To look into this, I first decided to see how a lightsaber was built. I went to alienryderflex.com and upon seeing how a light saber was built, I decided that not only could it NOT cut The One Ring, It could not even cut a weed out of your garden.
I was then curious as to what could cut The One Ring, that has been invented in the modern age. The solution came to me quickly. A Blendtec Blender.