How can I change the narration of Dubus' "The Curse" to the perspective of another character, say to the perspective of the victim?
The narration is normally called the point of view of a story, but we'll use your term for this answer. Changing the narration in this type of story is very difficult to do because to do so creates a whole different story. The situation and moral question examined become entirely different ones.
In this case, the narrator's perspective is individual, seeing only one victim and one problem. The victim's perspective would be panoramic, seeing all of society in a broad, multileveled problem. With a change in narration to the victim, not only is she attacked, she is left to fend for herself by a roomful of society's on-lookers.
The moral question of how one man should act in a specific situation would become, from the victim's perspective, the moral question of how society can act as it does. There would no single individual experiencing and representing one narrow social experience. The end result of the curse is originally individually felt, whereas, from the victim's perspective, the curse would be socially global, thus unfelt.
One way to get around this might be to develop a relationship between Mitchell and the victim. Give them a particular friendship. Have them be old acquaintances. Have her stop in regularly for change or a newspaper or a quick drink on the way home or to a regular bridge game or some such. This way, when she becomes the victim, she will automatically turn to Mitchell as her source of salvation. She can register the looks in his eyes, the expressions on his face, the actions he does or does not take.
Of, course, this will significantly change the style the story is written in: you will need dialogue to establish their relationship, and the story is originally written with minimal dialogue. These changes, however, will allow you to keep the same situation and to ask the same moral question: What will one man do? How should one man act in a given situation?