Depending on how much of the cable was left on our end, it could have a significantly greater impact than Mir...
Mir fell from outer space, through all of the atmosphere, and mostly burned up...
This cable would likely get extremely hot on its fall, and perhaps the highest end would get melted away, but a large portion of it wouldn't fall through enough atmosphere to disintegrate before hitting Earth...
Since the cable is very thin, it'd probably burn up a lot quicker than other stuff- more surface area and not much substance to provide impacting-ness.
Mir fell from outer space, through all of the atmosphere, and mostly burned up...
This cable would likely get extremely hot on its fall, and perhaps the highest end would get melted away, but a large portion of it wouldn't fall through enough atmosphere to disintegrate before hitting Earth...
Heck, even the bottom 1000 or so feet of it would be enough to cause a large amount of damage to the base below...