According to the source novel, he pretends to be deaf and dumb because it allows him to hear the secrets of the people around him.
They laugh and then I hear them mumbling behind me, heads close
together. Hum of black machinery, humming hate and death and other
hospital secrets. They don’t bother not talking out loud about their
hate secrets when I’m nearby because they think I’m deaf and dumb.
Everybody thinks so. I’m cagey enough to fool them that much. If my
being half Indian ever helped me in any way in this dirty life, it
helped me being cagey, helped me all these years.
This odd behaviour stems from his childhood and beyond:
It hadn’t been just since I came in the hospital, either; people first
took to acting like I couldn’t hear or talk a long time before that.
In the Army anybody with more stripes acted that way toward me. That
was the way they figured you were supposed to act around someone
looked like I did. And even as far back as grade school I can remember
people saying that they didn’t think I was listening, so they quit
listening to the things I was saying.