The mood of this story is one I would describe as ironic and darkly humorous while still retaining a core emotion of tragedy. All the characters have a varying degree of detached misery. As a way to cope with their grief, the characters over intellectualize their emotions to an almost farcical degree, adding a dark sense of humor to a tragic situation.
The ironic feeling of the story reaches its peak when the fat man gives his speech. He makes a rhetorical argument that it is actually better for their children to die filled with valor than to grow old and see the ugly side of life as he believes he has. This serves as an ironic punctuation to a series of arguments about who among them has suffered the worst.
The mood of the play lapses into one of stark tragedy at the very end, where the silent woman asks the fat man if his son is truly dead. The fat man realizes how easily his carefully built wall of rationalization can be broken and breaks down into sorrow.