You can exclude a mailbox from backups of an Exchange Online app.
Excluding a mailbox does not delete the mailbox from the app, but the mailbox is not backed up.
Procedure
From the navigation pane, go to Protect > Applications > Office 365.
The Office 365 apps page appears.
In the Name column, click the app that contains the mailbox that you want to exclude.
The app page appears.
In the row of the mailbox that you want to exclude, click the action button
, and then select Manage > Exclude from backup.A confirmation dialog box appears.
Click Yes.
Tip: To see excluded mailboxes, on the Mailboxes tab, click the gear button 
, and then select Clear all filters. In the table heading row, click any Column Settings button 
, and then select Columns > Status. The Status column is added to the table. Excluded mailboxes have a status of Do Not Backup.