maybe have guns on the ground or in orbit that can target the larger chunks. Or an orbital shield. Or the elevator could be exploded on every level and detach into smaller chunks that will burn easier in the atmosphere. Something? but its just a tv show so its okay :)
The worse part is the 54 month trip to Terminus. Holy fuck that would be so boring. Even with the holodecks.
Burning up in the atmosphere is no good. The tether has to be strong enough to withstand the strain of the atmosphere and all those different orbits on a daily basis, as well as handle the load that it carries. Otherwise the tether would snap or burn up during normal operation. So any material you used would be too strong to burn up in the atmosphere.
You also don't necessarily want to blow up the station to smitherines because the station itself is likely still mostly good and fixing it up again would be cheaper than building a new one. Even with the tether cleanup costs. Also blowing it up pollutes the orbits with smaller particles of space junk which would be more tricky to clean up and delay fixing the elevator.
Separating the tether might work. Sever it at the atmoshere and a couple more times in different orbits. Though damage would be harder to control. It might honestly just be easier to plan for the tether breaking and letting it wrap around the planet as a best case scenario. Alternatively I guess they could sever at the atmosphere, attach thrusters to the tether in orbit and launch it into the solar system. That would be fun.
And yeah, that 54 month trip is absolutely torturous. Atleast they do have those holodecks.