This Ableton tutorial covers the Live Input feature in Granulator III, showing how to route audio from another track in Live or an external source, like a microphone or hardware synth, directly into the device for granular processing.
Clicking the I/O button opens source selection, and hitting Capture grabs a snapshot of incoming audio at whatever length the Length parameter defines. That captured audio is immediately playable and manipulable inside Granulator III, just like any loaded sample.
One detail worth noting: the captured audio is temporary by default. To keep it with your project, you need to manually save it to disk using the Save button, otherwise it won't be there the next time you open the set.