Damaging Elevator
It depends on where on the elevator the terrorists hit. The elevator has to go from earth surface to some distance past geosynchonous orbit to keep the cable tight. A break near earth would cause the whole thing to fly out from centrifugall force, a break towards the middle and the outer sections flys away and the lower section collapses like a series of meteroids smashing into earth. There are several sci-fi stories based on a space elevator; the one I think of for this problem with space elevators is Kim Stanley Robinson's Mars series "Red Mars", "Green Mars" and "Blue Mars" about terraforming Mars.
