The tale is told to Yudhishthira in the forest books, in answer to a question about whether any woman ever equalled Draupadi in devotion, and its whole force lies in the dialogue rather than in any miracle. Savitri prepares by keeping a fast of three nights before the appointed day, and on the day itself she goes with her husband to cut wood and holds him as he dies.
When Yama takes the soul and walks away, she follows. He tells her to turn back; she answers that walking seven steps beside someone makes them a friend, that the good are worth following, and that a wife's duty is where her husband is. He is pleased and grants her a boon, excluding her husband's life. She asks for the restoration of her blind father in law's sight, and follows again. He grants another; she asks for the return of his kingdom, and follows again. She asks for a hundred sons for her own father, and follows again. Each time she pays for the boon with a further short speech on righteousness that Yama cannot fault.
Then she asks for sons by Satyavan. Yama grants it, and the trap is shut: she has not asked for her husband's life, and he cannot give her children by a dead man without giving the man back. He returns the soul, and she carries it back to the body before dawn.
The story is therefore not about a woman softening death. It is about a woman conducting a legal argument in front of the judge of the dead and winning it on the terms he set.