It appears that you have a few outgoing email messages that aren't being sent. You're receiving a message that you can't use the server. Since you're not able to send them, you'd like to remove them, but you're not sure how. I'm happy to help.
If a mailbox is offline in Mail on Mac -- Take your accounts offline by selecting from the Mail application Mailbox > Take All Accounts Offline, then see if you're able to delete the emails in question.
If you can't send emails using Mail on Mac -- If the issue persists, follow the steps below:
If the Send button is dimmed in the toolbar of your message, or your message can’t be sent using the outgoing mail server, try these suggestions.
Make sure the outgoing (SMTP) mail server is specified as directed by the provider of your email account. For more information, see Verify an account’s outgoing mail server.
If you see a message that you need permission to send an email, your account uses parental controls. For more information, see Request permission to send messages.
Choose Window > Connection Doctor, then follow instructions displayed in the Details column.
If there’s a firewall problem, verify that firewall software isn’t blocking email traffic on port 25, 465, or 587. Also check whether you’re affected by another firewall, such as software installed separately from macOS or built into an Internet sharing router, or administered by your email account provider. Contact the appropriate person for information.
You may be able to send messages from only a certain location, or your email account provider may allow you to send messages but with stricter settings (such as requiring a name and password). Contact your provider, then change the outgoing mail server settings in Mail preferences as needed.
Let me know how that goes.