No can Do, you can not delete them. 

But you can turn them off ( from settings, didn't try myself) 

I think they are the most useful feature of Community almost every thread I have replied or created, i get notified if there is any Change. 

@SweetTasha 

Go into yout profile click the 3 dots on the right and mark all as Read.

https://www.dell.com/community/notes/privatenotespage

Please press the Blue Accept as Solution button below if this answers your question.

@SweetTasha  If you mean the Bell icon shows a number (eg "8"), just double-click the bell which opens your Notifications page. All new notifications will be marked with a blue vertical bar on the left side.

Regardless of whether you click any of the new notifications or not, the number will be cleared from the Bell icon, and the blue bar will be gone from "old" notifications the next time you open the Notifications page. The blue bar will only appear again if there are any new notifications since the last time you looked at that page.