Taking down pages without deleting folders

I'm a new lab tech in a research lab at a university and have been in charge of creating a new website. I did so via a third party and had my current site redirected to that website. However, the old website still technically exists when you search it in google or manually type in the URL for specific sub pages. How do I go about deactivating those pages (i.e. removing them from searches, URLs no longer existing if you type them in, etc.). Do I just have to delete all folders, or is there a way to deactivate them?

Taking down pages without deleting folders