To remove the file, enter git rm --cached:
git rm --cached giant_file
# Stage our giant file for removal, but leave it on disk
Commit this change using --amend -CHEAD:
git commit --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
Push your commits to GitHub:
git push
# Push our rewritten, smaller commit