how to disable iCloud for Earthlink mail When I received a RED warning from Earthlink that my server mailbox
was full and that incoming mail would therefore be rejected, I went to my server's mailbox and deleted all the mail which I had already downloaded to my Macbook. When I returned to my mail application on my MacBook running High Sierra 10.13.6, all the previously downloaded mail was deleted as well. How can I empty my server's already downloaded mail without iCloud deleting that same mail in Macbook?  

My email is on an IMAP server structure.
IMAP keeps all email centrally. Deleting from any device deletes all copies, unless you archive them on one machine first.

To prevent IMAP from deleting all copies of its synchronised mail structure, you must first move any emails you wish to keep to a local folder on one machine eg.  from Inbox to a local folder inside "On My Mac".

To recover them, you would have to check either Time Machine - which you can do from inside Mail itself, by selecting your inbox, then from the Time Machine menu bar icon, Enter Time Machine - or see if your ISP has any method of recovering deleted mails.