If you prefer to delete emails rather than archiving them, there are several ways to delete emails in Mailbird.
1) Delete by right clicking an email in the Message List pane and select Trash or use the # keyboard shortcut which moves the email to the Trash folder.
2) Delete using the Scroll Action Bar that appears when you mouse over the profile pic or avatar for that email conversation. Click on the Trash icon to delete the email or conversation.
3) Use the keyboard shortcuts to delete emails by either going to the top left "Mailbird" dropdown menu in the main window > Shortcuts or hit Shift + ? This pulls up all the list of shortcuts. Search for Delete to find all keyboard shortcuts associated with Deleting an email or conversation in Mailbird.
To delete emails forever, please reference https://mailbird.zendesk.com/entries/21996535-Delete-Emails-Forever for more information.