Slaughterhouse-Five is explicitly anti-war, with a tone critical of ever-present conflict. At the same time, however, there is frequently a comedic tone, with zany and ironic situations creating humor no matter the gravitas of the situation. The overall tone is one of resignation and detachment, with Billy Pilgrim often appearing apathetic as a result of the fact that he knows his future with certainty.
Pilgrim's extraterrestrial encounter contributes to this apathy, as the Tralfamadorian viewpoint urges humans to look at the good and ignore the bad because the bad has, is, and will always happen. The anachronistic structure of the novel also contributes to the apathetic tone: the constant movement through time and place makes any one time or place seem not particularly important. Similarly, Pilgrim and the Tralfamdorian's anti-free will attitude supports Pilgrim's detached nature. As they both say after mentioning death, "so it goes."
The tone does change somewhat with the point of view: when the story is told from the perspective of the narrator, the tone is self-deprecating and comfortable. When the story is told from a third-person omniscient point of view centering on Pilgrim, it is comic and detached. The overarching tone of resignation and apathy, however, dominates the novel.