The point of git is that the history is embodied in each commit by hashing the parent commit. You could "replay" the commits (this is essentially how the svn-importer works) into a new repository and only keeping each sub-project. This, however, would destroy the meaning of the commit hashes. If you have no problem with that then so be it.
In the past I've just cloned it and moved on. This makes things larger but disk space is cheap; my time is expensive.
I also don't know of any tools to splice out a directory. I suppose you could git-log on the directory to find all commits on it then replay the commits with something like git-fast-export?