Hi Patrick,
According to your description, my understanding is that you want to disable an alert for all users at a SharePoint Online site.
In Site Settings->Site Administration->User alerts, there is a user drop-down list, you can switch the user to see the alerts for this user at the site, then you can delete the alerts that you don’t need.
If the list or library doesn’t have a lot of data, you can try to create a new list or library with the same data, then delete the original list or library.
As this issue is related to SharePoint Online, I suggest you create a new thread on Office 365 forum, more experts will assist you with SharePoint Online.
Office 365 forum:
http://community.office365.com/en-us/f/default.aspx
Best Regards,
Wendy
Wendy Li
TechNet Community Support
