I'd recommend foiling it, rather than clipping. A grounded (0V) metal wrapping will become a Faraday cage. It's a bit more effort, but is reversible, if you so choose. E.g. when selling it. It is also less likely to trigger a fault sensor condition, and doesn't void the warranty if the computer craps out.

How well does clipping the antenna actually work?

If my FM radio antenna rusts and falls off, my FM radio still works. Reception will be shitty but it’s absolutely still usable for nearby or powerful stations.

When the GPS antenna inside my much-abused phone came loose, GPS got very unreliable but still often worked in a glitchy way.

If I clipped the external antenna on a car’s cell modem, would it not be the same way? Based on my experience with those other kinds of antennas I’d expect maybe the manufacturer would lose the ability to track me while driving in remote or mountainous areas, but generally in cities or highways it would still connect. Is it not so?

Don't forget to swing it and make the swishy noise.