Deleting emails from multiple Apple devices

The only way is to use an IMAP mail server. The IMAP mail server centralizes mail so you can delete or mark a message as read on one device and it will be reflected on all devices that use the same IMAP mail.

You are probably using a POP mail server which downloads new mail and stores them on the device. Each device will download their own copy and there is no communication between devices if any mail is read or deleted.

Most mail servers will give you the option to choose which type you want, it is just set up in Mail differently. After confirming your mail server offers IMAP, you will have to delete the current one, then when adding back use the IMAP option, which is usually the default in the Mail app.