[Novocrane]

Stargate had an idea that I think could be what this monowire grenade is supposed to function like, it would just need strong anchors on the ends of the monowire and propulsion to shoot them out when the grenade reached its desired central tether point:

Sounds more like the instant snare, which creates a microwire web 6m in diameter. Spy Games.

[Anarkitty]

Well, hurricane winds have been known to drive low mass objects into trees and concrete... both of which are much denser then flesh... so I guess the grenade could work, depending on the velocity of the explosive used, given the low fricton level of the monowire....

But by anarkitty's math, it does seem unlikely.

That is a one-in-a-million fluke when it does happen, which is why it's interesting enough that you hear about it.  What you don't hear about is the millions or billions of other pieces of straw or sticks that hit that wall at the same velocity and simply were pulverized to dust. 
The same concept would apply here.  If one in a thousand, or even one in a hundred, of those grenades might manage to do some real damage under optimum conditions.  That still means it is not a reliable enough weapon to be worth manufacturing, especially since even if it works it's not really any better than a fragmentation or Hi-Ex grenade.

The Stargate version seems more plausible as far as the physics go, but the technological requirements are maddening: How long is each of the monowire strands and how do you keep them from hanging slack or catching before the attached anchor hits anything?  How do the anchors reliably bite into what they are hitting?  How do you throw the anchors out without an explosion large enough that it might as well just be a frag grenade anyway?

Also, remember there is a difference in SR between the monowire used for climbing and the monowire used in monofilament weapons. 
Weapon-grade monowire is thinner, more expensive and (presumably) has a lower tensile strength.
Climbing monowire will still cut you if you try to hang from it in bare hands, but just picking up a strand carefully shouldn't hurt you and even with a weight on the end swinging it around wouldn't make a very effective weapon.  Think 50Lb.-test fishing line that can actually hold 1000Lbs.
The Instant Snare is probably the latter, although I don't have Spy Games to reference, because if it was the former it wouldn't be called an "Instant Snare", it would be called an "Instant Blender" or "Instant Salsa-Maker".

[Reaver]

The tensile strength of the monowire in SR could in fact be VERY high depending on what it is made from.

Carbon nanotubes have a tensile strength of something like 16 times that of steel. (Not to mention voltaic storage properties!)

[Anarkitty]

Yes, but like everything, if two wires have the same basic materials and structure, they can only be made stronger by getting thicker.

A monowire in a whip is likely a single strand because the priority is on cutting power.  So thin you can barely see the wire except for a glint in the air.  You wouldn't want to try and swing across a pit on it like Indiana Jones, though.  If it doesn't cut through whatever it is wrapped around, there is a good chance it wouldn't support your weight and snap, or the motor in the handle that retracts the line would give out.
A monofilament rappelling line has less emphasis on cutting things (in fact, you don't want it to usually) and more on balancing strength with weight and bulk, meaning a thicker strand.  It is designed to not cut, because that would defeat the purpose of tying it to something to support you.  It is thin enough to cut your hands if you were to hang from it without gloves, but it isn't going to slice through your leg if you walk into it.  It makes a good garrote or trip wire, but not a weapon.

[Novocrane]

Just to clarify; the rappelling wire and the whip wire are somewhat different - microwire and monowire, respectively.

Microwire: This micro rope is made of an extremely thin (nearly monofilament) and resilient fiber; a great length of it can be stored in a very small compartment, and it is very difficult to see. The downside is that it can only be grabbed with special protective rappelling gloves without slicing straight through the climber’s hands, inflicting 8P damage with an AP of –8.

[Anarkitty]

Ah, thank you.  I didn't have my rule book at hand and my memory did not server me perfectly in this case.

"(nearly monofilament)" is telling.  It means it is probably similar to a braided cable made of multiple monowires.

It sounds like RAI it is only supposed to do the damage if you try to use it for climbing without the special gloves, but RAW it potentially does damage any time it is "grabbed" which means it would be quite effective as a trap or possibly even weapon in a pinch. 
I would even let a player with monofilament whip skill use a microwire climbing line with a weight on the end as an improvised weapon but it would do less damage.

[Insaniac99]

"(nearly monofilament)" is telling.  It means it is probably similar to a braided cable made of multiple monowires.

At that price, I sincerely doubt it.  It is more likely similar but completely different material.