Snipping off just the first few kilometers is not catastrophically destructive yet, and cutting it down further up would require multistage rocket designs, sophisticated steering/targeting and potentially significant yield (you'd need to cut unobtainium, after all...). If you can build a space elevator, you can defend against those.
You better thoroughly inspect what cargo you put on the elevator itself, of course.
Snipping off just the first few kilometers is not catastrophically destructive yet, and cutting it down further up would require multistage rocket designs, sophisticated steering/targeting and potentially significant yield (you'd need to cut unobtainium, after all...). If you can build a space elevator, you can defend against those.
You better thoroughly inspect what cargo you put on the elevator itself, of course.