Cacher is the code snippet organizer for pro developers

pushd <big-repo>
git subtree split -P <name-of-folder> -b <name-of-new-branch>
popd

mkdir <new-repo>
pushd <new-repo>

git init
git pull </path/to/big-repo> <name-of-new-branch>

git remote add origin <git@github.com:my-user/new-repo.git>
git push origin -u master