Extract directory from the GIT repo to the standalone GIT repo.

split_repo.bash

#!/bin/bash
FROM=$1
TO=$2
echo "Spliting '$TO' from '$FROM'"
git clone --no-hardlinks $FROM $TO
cd $TO
git filter-branch --subdirectory-filter $TO HEAD -- --all
git reset --hard
git gc --aggressive
git prune
echo "DONE!"

Here's a relevant question on StackOverflow (probably the source of the above script), with additional tips and variations:
http://stackoverflow.com/questions/359424/detach-subdirectory-into-separate-git-repository