What did Colonel Kurtz mean by his story of a snail on a razor?

Well, Kurtz is quite literally mental, which is why the Army has sent in a special task force to take him out.

He's essentially saying he wants to experience life's harsh events, even traumatic ones, and come out alive. He wants to know he can take anything that's thrown at him and still live.

However, this also includes a bit of foreshadowing. The line is from a tape recording Willard listens to before being given orders to find Kurtz and take him out. When Willard finally does kill Kurtz, it's while Kurtz is making another tape recording, during which Willard hacks away at him with a machete.

He was drug across the edge of a blade, but unlike the snail he wasn't able to survive.

UPDATE:

Holy cow, talk about finding something randomly that can also add/enhance an old answer of mine.

So apparently, as shown in this video, snails can crawl along the edge of blades without injuring themselves, which adds credence to Kurtz's desire to do something this creature can that humans cannot.

https://vimeo.com/65745551

No, the Viet Cong is the snail. They have come against the most powerful military machine in the world, the razor, and emerged unscathed.

• It is his dream, because as a special forces operative, that is his idea of perfect warfare.

• It is his nightmare, because it renders the US vulnerable to SE Asian peasants.

(actually it also reminds me of the scene in Star Wars where the Millennium Falcon rests against the side of the Imperial ships' radar - it is too small to be caught and found)

It also becomes his dream because he sees the only way of combating it is to create his own force along those lines, using locals and treating them as harshly as the VC treat their own; "to kill without feeling ... without passion ... without judgment". This becomes evident when he discusses the incident where the children's arms are cut off :

I've seen horrors ... horrors that you've seen. But you have no right to call me a murderer. You have a right to kill me. You have a right to do that ... but you have no right to judge me. It's impossible for words to describe what is necessary to those who do not know what horror means. Horror. Horror has a face ... and you must make a friend of horror. Horror and moral terror are your friends. If they are not, then they are enemies to be feared. They are truly enemies.

I remember when I was with Special Forces. Seems a thousand centuries ago. We went into a camp to inoculate the children. We left the camp after we had inoculated the children for Polio, and this old man came running after us, and he was crying. He couldn't see. We went back there, and they had come and hacked off every inoculated arm. There they were in a pile. A pile of little arms. And I remember ... I ... I ... I cried. I wept like some grandmother. I wanted to tear my teeth out. I didn't know what I wanted to do. And I want to remember it. I never want to forget it. I never want to forget.

And then I realized ... like I was shot ... like I was shot with a diamond ... a diamond bullet right through my forehead. And I thought: My God ... the genius of that. The genius. The will to do that. Perfect, genuine, complete, crystalline, pure. And then I realized they were stronger than we. Because they could stand that these were not monsters. These were men ... trained cadres. These men who fought with their hearts, who had families, who had children, who were filled with love ... but they had the strength ... the strength ... to do that.

If I had ten divisions of those men, then our troubles here would be over very quickly. You have to have men who are moral ... and at the same time who are able to utilize their primordial instincts to kill without feeling ... without passion ... without judgment ... without judgment. Because it's judgment that defeats us.

– moviequotedb.com

It ultimately becomes his nightmare because the CIA are still able to get in there in kill him; in the form of a single man. A larger force would have attracted too much attention and been destroyed by either him, the VC or the NVA.

Kurtz foresees his own death.

He foresees Cpt. Willard character (the "snail") winding it's way through the jungle on a dangerous mission ("crawling on razor") until Willard ultimately encounters Kurtz ("and surviving"). Kurtz both longs for and fears his death (it's my dream, it's my nightmare).

Incrementally a lowly snail surmounts the sharpest blade. A reflection of the PREPONDERANCE OF THE SMALL.

He's talking about American foreign policy and how it is fatalistic in nature. He sent it so that it would be intercepted. He's telling them that America is the snail, and the way we conduct foreign policy is the straight razor. The real horror to him is that we won't be undone, that we will continue to do what we do without consequence.

I've always seen it as Kurtz's observation of humankind's persistence in war, at the personal level and on every other scale.

Struggling ever forward on an excruciating journey, which once embarked upon must surely lead to inexorable doom and yet somehow, by not deviating from that path, continuing to avoid utter destruction.

To be or not to be... To sleep ... Perchance to dream... Krurtz has turned himself into one able to slither across razors without harm... From anyone but himself... Will he be able to endure a return to modern civilization after experiencing full blown will to power? Many vets experiencing just a small part of being able to summon fire from the sky were unable to handle the pressure. THE GOLDEN BOW.... the King of the Woods guarded the sacred Oak Grove and was constantly vigilant for was always challenged because it was of the utmost importance for this priestly King to be the strongest and deadliest man alive.... whoever succeeds in killing him takes his place... It is an indignity for for the King of the Wood and everyone if he continues on at less than the apex of power.

Actually I think it means that Kurtz is the snail slithering on the edge of a straight razor. The war and how he fights it. If he falls the wrong way and fights it ethically morally he may lose the war. If he falls the other way and fights to win then he will order anything to win The end justifies the Means. But he and all that follow him will lose their humanity. The very reason that they fight for. So while he stays on the edge he survives the bureaucracy of those that send him to fight the enemy.