I want to remove a file from my repository.

git rm file_to_remove.txt

will remove the file from the repository, but it will also remove the file from the local file system. How do I remove this file from the repo without deleting my local copy of the file?

The git rm documentation states:

When --cached is given, the staged content has to match either the tip of the branch or the file on disk, allowing the file to be removed from just the index.

So, for a single file:

git rm --cached file_to_remove.txt

and for a single directory:

git rm --cached -r directory_to_remove