To avoid loosing messages it's important to do this while the server is stopped, however with a large domain this will take too long. So instead do the copy in two steps, on windows for example:
before changing the drive copy the bulk of the contents to the new location
robocopy c:\surgemail\mbox\domain.name d:\mbox\domain.name /e /copy:DAT /mt /z /purge
Then stop surgemail, and change the mailbox_path setting for that domain in surgemail.ini
And re-run the robocopy command to apply any changes since the first copy
robocopy c:\surgemail\mbox\domain.name d:\mbox\domain.name /e /copy:DAT /mt /z /purge
Now restart surgemail.
(This is for windows, you can do the same thing using rsync on linux)