In "A Worn Path," why is it significant that the grandson cannot speak?
The grandson does not appear in the story. The fact that he has no voice illustrates his helplessness. "Having no voice" has a lot of implications and interpretations, some of which may be quite fitting or irrelevant to this story. For example, politically speaking, having no voice implies that one has no political power as a voter, democratic citizen, and so on. It could even imply that one with no political voice is oppressed in some way and/or is treated as a lower class citizen. Given the racial elements in this story, one could argue that the grandson's lack of a voice is symbolic on a racial and/or political level. His generation and subsequent generations will not have "voices" as long as they are treated like second class citizens. (Note that the people in the town treat Phoenix condescendingly, like a charity case.)
He literally has no voice because he had swallowed lye when he was younger. This damaged his throat. He depends upon his grandmother to get his medicine to sooth the pain and open his throat. His lack of a voice illustrates how helpless he is. The image of this helpless boy, with no voice, also fits the symbolism of the story. According to Phoenix, he waits for her, "holding his mouth open like a little bird." Phoenix's name is symbolic of the mythological phoenix (Greek myth), a bird reborn again and again of its own ashes. She continues to make the journey again and again, despite her old age. It is symbolically consistent that she is like the mythological phoenix (a bird) and the grandson is also like a "bird."