The instinct to not just delete is correct, because departed employee mail usually still matters for a while, so the right pattern preserves before it stops, in stages by how gone each person is:
The immediate stop with grace: disable the AD account to end their access, then set the mailbox to reject or redirect new mail. Redirecting to their former manager via forwarding, without keeping a copy, means legitimate senders reach someone who can help while the dead mailbox stops accumulating, the arrangement most departures actually want for the first months.
The preservation before removal: while the mailbox still holds their history, export it to PST with New-MailboxExportRequest -Mailbox user -FilePath \\server\share\user.pst, giving you the archive legal and business continuity may need, stored per your retention policy. This is the step deleting first destroys, so it comes before any removal.
The clean rejection when the person is fully gone and preserved: rather than a mailbox lingering, a mail flow decision, either remove the mailbox after the PST export so mail to the address bounces with a clean NDR or keep the address alive as a forward to whoever inherited the function if customers still write to it. The bounce tells senders honestly the person left, the forward keeps a business relationship from hitting a wall, chosen per whether the address was personal or functional.
The systemic fix the accumulation reveals: an offboarding checklist that disables the account, exports the PST, sets the forward or bounce and schedules the removal, run at each departure, turns this recurring cleanup into a solved process rather than an annual archaeology of who left when.