The death of a thousand cuts refers to Lena's fantasy about the punishment to a traitor. The traitor had thought pusnishment was the worst thing he could have experienced but he was wrong. The fantasy is found in Lena's chapter "The Voice From the Wall".
The cuts symbolizes to the worst possible thing than can happen to one person. The cuts that Lena speaks of are not always physical; cuts to one's spirit and identity have the same effect. This may explain why Ying Ying has her break down after the death of Lena's baby brother.
Throughout the chapter, Ying Ying is hypersensitive to the dangers of the world. She continually warns Lena of the dangers lurking around her. Each percieved threat eats at her, taking a bit of her spirit away. Also Ying Ying has had a rough life before arriving to America (loss of her upper class status, loss of her first husband to an afair and then to death, her rightful name and birthdate) that also cuts into her as well. When Ying Ying loses her child, that is the last cut that breaks her hold on reality. This is the worst thing to happen to a person, in Lena's mind.
But Lena has hope that her mother can come back to her. Like the story that starts the chapter, Lena's hope is that since her mother has experienced the worst thing that can happen to a person, her mother will no longer be afraid and learn that her previous fears were unfounded.