How do I delete an iCal event without sending notifications?

You can move the event to a local calendar. When deleting you will then get the additional option "Delete & do not notify".

In the end, I created a new calendar specifically to move event invites to, which I don't want to see anymore. Then I hide that calendar.

As Feuermurmel says, you can create a new calendar and move it there. But instead of hiding the new calendar, you can just delete the calendar. Worked well for me; the event is gone with no notifications.

I ended up doing the following:

• create a new iCloud calendar
• select the invite, and chose the new calendar in the calendar drop down on the info pane on the right
• select and right-click the calendar on the calendars pane on the left and chose delete
• pick the option delete and do not notify

I hope this helps.