The cable you picked up was probably "Guy Strand". I have manufactured many thousands of miles of it, and it is used extensively in the utility fields. It is a lot easier to cut than it's "Prestess" counterpart. The galvanizing lowers the yield strength of the cable.
Instead of cutting it, if you run over it again, try watching for that type of obstacles when mowing. However, if you get it wound up dispite being careful, I would remove the driveshaft, and use the loose end to unwrap the cable by slowly pulling it with the tractor, allowing it to unwrap itself. That is what has work best for me. Barb wire is more commom, and doesn't unwrap as easily as guy strand. The nuts on the bottom of my gearbox often get in the way of the unwrapping.
A hacksaw will probably not be a good idea, since the tensile strenth of guy wire is around 170K.
Good luck,
David from jax