I am able to clone the Android source code by using the "repo" tool. However, what I want to do is clone the source code in a more minimal way than having an 11GB footprint. It seems to download things related to every Android device and every prior release. I tried thought I could reduce this by checking out a specific branch like this:
repo init -u https://android.googlesource.com/platform/manifest -b android-4.0.1_r1
However, what ends up happening is that I still get everything involved, just at a specific snapshot (understandable). But is there any way to limit the amount that is cloned?
The android source tree is made up of many separate git repositories, which are all managed by repo. You can't really reduce the amount of data that's downloaded for a given git repository.
However, you can only download a subset of the git repos that are available, using repo sync <project>. I.e. if you only wanted the frameworks/base package, you should be able to do repo sync frameworks/base, after doing the initial repo init.
If you are actually wanting to build the source though, you probably want the full thing.
You might be able to save a gig or two by removing the device repositories that you don't need. You can do this by editing <source>/.repo/manifest.xml and removing the repositories for the devices you don't want.