The poem "Barbie Doll" by Marge Piercy is less about physical death and more about the death of what the real ideal of women should be.
The girlchild represents you and I: Typical, ordinary, and everyday women who have great qualities and normal weaknesses. The girlchild is born with qualities that are ordinarily considered good. However, in the type of setting where this poem develops, it is understood that women are not meant to be strong, skilled, nor intelligent: They are supposed to look good, act cute, and be seen but not heard.
The girlchild in this poem does not understand why she has to give up what she considers to be the qualities that make her unique in favor of changing them for a plastic and superficial society. She cannot fathom what could be wrong with her, but she is consistently told that everything is wrong.
Hence, the moment when she "gives up her nose and her legs", does not refer to an actual and literal cut of her body parts. It is symbolic of how she had to relinquish the pride she felt for her uniqueness, and how she allowed herself to believe that her big nose and her thick legs were not good enough. It means that she now believes that there is something wrong with her. Or, perhaps, that she changed her nose and her looks in order to be considered "OK" by everyone else.
Her funeral is symbolic of the death of her real self. The real woman is gone and, in her place, society has given her what it feels she lacks. Now she is exactly as they expect but, in her own flesh, she is dead.