I think you're talking two separate issues here, deactivation after certain kinds of events, and physical removal from the aircraft.
Deactivation can easily be accomplished by pulling the applicable circuit breaker(s) and that will preclude the recording over the event by ambient sounds occurring after the event. I can readily recall where a Valujet DC-9 that had a landing accident at BNA
(landed short of 02L due ground spoiler deployment in-inflight, got airborne again, and came around to the right for a straight-in to 31 and stopped it there on the runway). Someone didn't pull the CVR breaker, and the original event was recorded over. The move from :30 minute CVR recordings to 2 hour recordings provides a little more time to secure things, as well as to record more of what happened prior to the event itself.
As far as removal goes, maintenance (company or contract) can do that, and chain-of-custody procedures followed as a part of whatever degree of investigation results.
ALL views, opinions expressed are mine ONLY and are NOT representative of those shared by Southwest Airlines Co.