When signing out of Outlook on the mobile app, you’ll encounter the same issue — there’s no simple sign-out option. You have to remove the email account from the app. For this guide ...
It might delete the email that is causing you trouble while ... Read: Email in Outlook not syncing? Repair Outlook account.
If Outlook throws message Repair Outlook, This will clear local settings and any unsaved Outlook data, understand what this means and what you need to do.