Just to throw this out there: imagine the forces a space elevator would have to bear to be viable. Don't just imagine what acts of terror could do to it, imagine the amount of force they'd have to play with just to do anything directly to it!
"Great, now we have a space-borne cable slicing through the Earth's crust. Oops."
There's an amazing sequence in Kim Stanley Robinson's "Red Mars" describing the destruction of a space elevator in a terrorist attack: the cable digs a trench marking the equator of Mars as it wraps around the planet multiple times.
"Great, now we have a space-borne cable slicing through the Earth's crust. Oops."