I'm not a big fan of wire saws but there's something that isn't taken into consideration:

The smaller the branch/tree/wood/ you are cutting, the smaller the radius is which the wire needs to wrap around. This makes the wire bend A LOT more each stroke and as anybody who's used a paper clip for it's non-intended purpose knows, this weakens the wire/metal.

As I recall, Les Stroud was trying to cut something far less thick than wrist size...I could be mistaken however.

Either way, there are quality version of these saws to be had made from materials which can handle the stress (more than the cheapos most of us are familiar with anyhow)...but I'm still not a fan.