Deleting a Company Profile

My company profile is out of date, where can I delete it. 

If you're the owner of the company profile, you can login and delete it in your Account Settings under "Manage Companies."

My profile is deleted, but it's still showing up in a Google search with a dead link. How do I get Google to stop showing that result?

That's something Google has to take care of on their end. Google has a rolling cache refresh that continuously updates their search results for different search terms. Usually when a link has been taken down it's only a few days before it's been re-cached and updated by Google. Once that happens the result will be gone.