Neither API, Mirror or GDK, will actually do the work of calling the remote server and getting a response - those are normal things that you should be able to do with the underlying tools they are built on (whatever platform you choose to develop with, if you're using Mirror, or Android if you're using the GDK).
What both APIs support, however, is helping you deliver that information to Glass in the most appropriate way possible.
The Mirror API is good for Glassware that is accessed over the Internet and work with the native timeline operations that Glass provides. The GDK is useful for more immersive or dynamic applications that don't necessarily work with the timeline or the network.