I had this need. I wanted to create an exact copy of an existing website, and put it in a subdomain, as an archive.
Now this site is under version control, and I wanted to retain the Git history but also deploy it to a new GitHub repo, so I could deploy it separately, now both sites could go on their own destiny.
The website is a Hugo site, so I just copied the website folder into a separate folder, and that was it, locally.
So I went into the copied site folder in the terminal, and I ran
git remote -v
this listed the existing GitHub repository as the "origin" remote.
I ran:
git remote rm origin
This removed the origin remote, so running git remote -v didn't return anything any more.
Now since I use GitHub Desktop I just dragged the folder in that app, and I was able to create a new, different GitHub repository from there.