When your mailbox is full, you can adjust the mailbox storage quota or clear the old messages on the server. Here are the steps:
Tools > Accounts. You will see a box open (named Internet
Accounts), click "Mail"
tab, click on the mail account, click on Properties > Advanced.
Remove the check in
the box "Leave a copy of messages on server."
You can also choose to leave the emails on the server for certain days:
Click on Tools > Account settings, click Server settings, remove the check in the box Leave messages on server to delete all old emails or set it as below to leave the emails on the server for 30 days.
Click on Mail > Preference > Accounts, then click the Advanced tab, check the box Remove copy from server after retrieving a message and select the time you want to leave the emails on the server.