Hi @Aaron Smyth ,
I am the Admin user on MS Office 365 and I would like to understand how to permanently delete emails to free up some space.
Before we continue, I'd like to clarify that the Recoverable Items folder has its own quota. See this link for more explanation. So, if what you are after is to free up the space of the user's primary mailbox, there's no need to deal with items inside the recoverable items folder. Instead, you can consider using other methods like adjusting the retention policy. You can also share the article below for users to manage mailbox size on their own:
Manage my mailbox size
If you do need to clean up the items in recoverable items folder to free up the recoverable items folder quota, you can follow the instructions in this document which has already been provided earlier by Michev.
When I delete emails in Outlook, they are able to be recovered. How do I delete these emails permanently?
The Recover Deleted Items feature available in Outlook is intended to allow end users to recover an email that is accidentally deleted from the Outlook mailbox. As far as I know, currently it's not feasible to disable this feature in Outlook. If your purpose is to allow users to permanently delete an item from Exchange Online, for user mailboxes that is not under any hold, you can disable single item recovery on mailboxes so that when users purge items from the Recover Deleted Items folder, these items would be removed permanently. Below is a document about Recoverable Items folder, you can go through it if you have the interest to dig deeper:
Recoverable Items folder in Exchange Online
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