Part of this is a legal or human resources question. Did the user leave on good terms or under a cloud of suspicion? Do other users taking over their role need access to files? Is email involved, and if so, is it subject to potential litigation? In an extreme case, could deleting their files be considered destruction of evidence? Those aren't technical issues.
On the technical side, disabling the account (not even deleting it) will generally block most access. I have to say "most" because today's mobile, connected world there are a lot of things being cached and synchronized. The user could use cached credentials to log in to a computer that is disconnected from a network.
One important technical issue to be aware of, is that ActiveSync (the most common way for phones to access Exchange) can allow access to the mailbox after the account is disabled. (See https://blogs.technet.microsoft.com/messaging_with_communications/2012/06/26/part-i-disabled-accounts-and-activesync-devices-continuing-to-sync/)
In cases of "urgent dismissal", I'd recommend having a checklist (which can then be scripted) that covers all of the technical and manual steps that you (the IT department) and others (people like HR, physical Security, etc.) need to do if someone leaves the company suddenly. That checklist can then be vetted and approved by management or legal as well. Some starting points are in that blog from Joe Schaeffer.
You can search for topics like "Termination Checklist" for samples.