Only way of doing that is by connecting a video cable to a TV (MHL is what should work for an S3), BUT that assumes that you still have touch input or a BT mouse previously connected.
Another way is to use Samsung Kies to back up your phone, but that needs it to be unlocked, and if you don't have a screen or touch input and your phone is locked, then that won't help either (although you can try to unlock remotely with Google's Device Manager or Samsung's Find My Mobile. If the phone is unlocked you can also back up your files to a PC as if you had an USB stick, but that won't work with texts.