In eclipse, there's just a button disconnect in popup menu selection "team" which can disconnect the project from the version control system like Git or SVN, and even can delete version control information like files in ".git" dir or ".svn" dir of the project.
I can't find the counterpart button in IntelliJ and don't know how to delete the Git information. I deleted the ".git" directory of the project, but opened IntelliJ again, it still show that the project is in Git and can't be pushed to new Git repo.
I guess that this could be a duplicate, you can find at least the first part of your question here
After that you remove VCS, you would be able to remove .git directory without any problem