In the case of a loosened cable string being struck, as opposed to being cut (as @Craig pointed out) is the effect of the momentum of the object striking the cable/string being lost as the loose object dissipates this energy. You see this in car races along the edges that use hay bails, or barrels of water, and behind those highway trucks that carry rows of plastic barrels filled with water to absorb the energy of an impact should you run into one.
All of this happens, or not, before any concern for snapping the struck material. So simply put, the blades did not have enough energy left after putting a loose item (string) in enough tension (as described above) to break. In the case of a taut cable/string, more/most energy of the striking object is put into cutting through it-as the cable/string would take more energy to make "tighter" than the blade has in it's momentum.
If the taut cable/string needed more energy to snap than the blade had in momentum at the point of contact, the blade-not the cable/string-would have to absorb all of the momentum/inertia of dropping to a speed of zero! What is worse (for the blade) is the fact that this energy needs to be absorbed at the very small point of contact/impact. Meaning that all that energy would be focused on the blade at a very small point (think lbs/sq.inch), resulting in maximum stress to the blade material at that point.
The larger the contact area, the less any one point has to absorb, and less damage will occur to the blade.
Sorry for the non-academic explanation.
"I'm no physicist, but I know what matters!" ~Popeye
P.S. In the case of scissors, the same principle applies, actually, in that a large amount of force is being applied to a small area (where the blades meet). There the energy is the same, but applied slowly. In other words, where energy is mass x speed, you can raise either one to get the same result. This is why bolt cutters have more 'handle' toward you, and only a little bit where the cutter is.. :)