If you manage a community, you'll get an email every time a new organisation asks to join your community. You'll be able to click on this email to say whether you accept or decline this request.
If an organisation is a member of your community, their published stories will automatically appear on your community website, and their events will automatically appear in your events calendar.
To remove an organisation from your community, go to 'Web Publishing', click on 'Communities I manage', and you will be able to see the organisations and projects that belong to your community, with the option to remove any of them. Removing them merely removes them from your community, not from interests.me altogether.