Lyric discussion by EmmettO 

Cover art for Cutting Stone lyrics by Decemberists, The

The only reference to a cutting stone I can find is Hippocrates' proscription to physicians in ancient Greece not to “cut for stone,” or to do more harm by cutting into a patient.

As I read through the lyrics, I wonder if the cutting stone is knowledge? In a way, it can "cut through" wire, wood and bone. You'll always have it and you can teach others so you can "Cut my cutting stone in two." You'd do this especially after reflecting over all the works you've accomplished.

Knowledge may be the wrong idea exactly, but it seems like something mental, exterior to the person. "Whether wild or whether won" could be different ways of learning. You just understood it intuitively (wild) or you learn it through effort (won).

"Cutting stone fear me none" could be anthropomorphizing knowledge, a call for it to not escape you.

"I'll cut you down, my cutting stone" is questioning what you know, cutting down what doesn't or hasn't worked. It could also be doubt in one's own understanding. Only new knowledge can cut down old knowledge.

The child is abandoned, he raises the child and his knowledge "did the rest" as in took care of them. Now this is where I kind of want a word other than knowledge. It kind of works, but wisdom would be better.

The suitor weeps and he consoles him. Again, cold knowledge doesn't feel quite right, but wisdom could. It could also be some philosophy that helps the suitor.

I could be wrong but it seems to fit.