If yes, how many nanotubes lined together would it take to make it impossible (or at least very hard, well you probably ask me to define hard - impossible for average human making one clean cut, without actually sawing them)?
I think a nanotube’s powers here lie in its tensile strength, not how rigid it is. I could be wrong though.
My WAG is about the thickness of a bungie cord.
Obligatory XKCD link
Think of it like hair or spider silk. They may be stronger than steel in terms of tensile strength per unit of weight, but you can cut them much more easily than steel at any thickness.
If nanotubes are really that soft doesn’t it defy its use as a material? I’m mean what’s the point of having really strong rope that will just wear out on the joining?
Using nanotubes inside a sheath of some sort or as part of composite matrix is where a lot of the research is directed.
Scissors beats nanotubes
Rock beats scientist.
Can we make nanotubes long enough to cut with scissors? I thought the longest now is a few mm. I’ve seen CNT before, they looked like soot.
Scientist writes paper.
I’m pretty sure we’ve got tens of centimeters.
So, about 30 cm down, and only 4,216,399,970 cm to go… c’mon space elevator!
A number of years back (I forget exactly when, but about 6 or 8 years ago) someone made a 10 cm nanotube. They then imaged the entire thing with an electron microscope.
The individual fibers don’t all need to be as long as the entire cable. Given sufficient money (admittedly, a metric buttload of it), you could make a sufficiently strong space elevator cable out of 10 cm fibers.
Of course, that metric buttload of money would probably be better spent on developing cheaper and more efficient ways of making nanotubes, than on buying up fibers made using current techniques.
This thread has taught me an important thing about the space elevator: I always imagined it as a physical structure - made of nanotubes - built from the ground up, inch by inch, like any skyscraper. Now I see that they’ll need to make a spool of nanotube rope, several dozens of thousands of miles long, and lower it from orbit. Yikes!
Most plans start with a mere thread of nanocable, strong enough to support only a few kilograms, launched into orbit. Then, you build a small robotic climber with a similarly-small spool of more nanocable, that climbs the original cable and lays down a little more cable along the edge as it does so. That climber is followed by another slightly larger one, that lays out a little more, and so on, until you’ve built up to a cable that can support your real, multi-ton payloads. You still need to make a pretty hefty initial launch, but you don’t have to launch the whole thing at once.
Likewise, once you have one cable big enough for payloads, you can use the same technique to build a second (or third or fourth) one for redundancy. And then you can manufacture cables in the vicinity of Earth and send them off to the Moon or Mars, or other destinations (you’d need a somewhat different device for the Moon or Mercury, but it’d still involve lengths of high-strength cable; space elevators similar to the one on Earth would work for Mars and the moons of the gas giants).
I’m confused. The space cable idea is that the thing has no anchor above, after the initial drop down, a la Chronos? Like the Indian Rope Trick?
Yes. It looks like magic–but it’s science! 
There’s an upper anchor above geosynchronous orbit which wants to fall away from the Earth, as it’s being drug along too fast an orbit for its altitude; and the whole thing, on balance, is stable. (Until the asshole with the pruning shears comes along.)
Wow I stop paying attention for a while and science has progressed so much. Have they by any chance become thicker too?
Regarding the original question, I think dracoi has it. CNT are strong, because they’re so tiny. If you bundle enough together to cut, you’re only cutting a few at a time, so it’s possible.
This made me think about unrelated question:
If you cut the line will it go straight up so people standing next to will be safe or maybe it will get some horizontal velocity?