Using New Outlook on Windows for personal email, calendar, and contact management
I had the same issue.
When you go in to the signature section, if you select the 'Email Account' option it will show your email and also a second option 'signatures on this device'. When I selected that option, the signatures I had deleted were still there. Deleted them from that box and it appears to have resolved the issue.
4. Select the signature you wish to delete and click Delete.
5. Click Yes to confirm.