Is there a way to separate a site inside a network (multisite) into its own wp site?

We might need more details, but I’m going to assume that you are using subdomains, and that you want to retain the site’s subdomain name on the new server. If that’s the case, then all you should need to do is export the site, then import it on the new server. Then set up a new DNS ‘A’ record to point that specific site name to the new server’s IP number. This should override the wildcard DNS domain pointer that multisite normally uses.

So, in your DNS setup, you should wind up with something like:

; DNS for example.com
*        A    111.111.111.111 ; multisite wildcard entry
foo      A    222.222.222.222 ; foo.example.com is on the new server

Make sense?

Depending on what else you’ve got going on, it might be more complicated. For example, you might have to search-and-replace in the .wxr export file to fix file paths for image uploads and such.