Removing a file added in the most recent unpushed commit

If the file was added with your most recent commit, you can delete the file and amend the commit:

git rm --cached giant_file

Then commit the change using --amend -CHEAD:

# Amend the previous commit with your change
# Simply making a new commit won't work, as you need
# to remove the file from the unpushed history as well
git commit --amend -CHEAD

Push to your remote repository:

git push

Or, if neccessary, force push:

git push --force