Require Admin level to mount removable media or network attached storage device
The traditional manner for locking down Macs was to use the MCX framework and Apple is in the process of removing that and moving to Profiles to control this sort of thing.

Both have mechanisms for limiting access to storage - internal, external, etc…

I would recommend you learn about Profiles since MCX has been on the way out since Lion arrived and should be considered for legacy OS and hardware at this point.

Here are two articles to get you started so you can decide what tool you might want to use for the job:


MCX: Client Wrangling 101
Mountain Lion Profile Manager documentation


You might also decide to get some software that helps automate the creation, distribution and most importantly, the reporting of compliance on an ongoing basis, but you could get started with one license of Server and a single Mac to test whether you want to use Profiles or find another solution for your Mac management.