First grant permission to the admin account
Add-MailboxPermission -Identity "John Doe" -User compsquareadmin -AccessRights FullAccess
Export message to pst file
Export-Mailbox -Identity "John Doe" -PSTFolderPath C:\Users\compsquareadmin\Desktop\john_doe_export.pst
Note: export to pst file require 32bit operating systemPerform the deletion
Export-Mailbox -Identity "John Doe" -StartDate "01/01/2015" -EndDate "12/31/2017" -DeleteContent"