In order to understand the tone of the story you must look at the point of view. The point of view of "To Hell With Dying" is that of a third person omniscient, relating back to when she was a child. Therefore, the tone is innocent, naive, and sometimes even comical, as it expresses how something as complex, sad, and obvious as death is seen through the eyes of a kid.
The narrator is now a grown-up, but during her childhood, her father and siblings would mock death by showing at an old alcoholic and decrepit sick man of the town, Mr. Sweet, the words "to hell with dying". These words were, in the eyes of the narrator (as a child) like a magic potion that would "resuscitate" the man and bring him back to life after many brushes with death caused not just by his naturally chronic state, but by his mindless self-medicating with alcohol.
Another thing to say about the tone of the story is, ironically, that it is refreshing. Aside from innocent, naive and even comical, the tone is refreshing because the story is related with the natural wonder and tenacity of children: death is a surprising, and not a depressing event. Sickness is a curious, and not a tragic reality. Old age is an expectation, not a life sentence. If this story were to be told through the eyes of an adult experiencing the situation, the tone would have been sad, depressing and negative
Therefore the fact that it is a child that tells the story infuses humanity, innocence and a sense of hope within the overall theme of death that permeates the story. It is that what makes the book appeal to both adults and children in such a way that the message that Alice Walker sends is clear: life is what you make of it through your very own eyes.