“The Man I Killed” begins with a detailed list of characteristics of the dead body of a young man who has died of a wound. What is the emotional effect of describing the dead body in this way? What is the emotional effect of O’Brien’s detailed description of the victim’s life? Why does he include these details? Does it matter that this may be “story-truth”?

The text you refer to is from Tim O’Brien’s anthology The Things They Carried, which tells fictionalized accounts of his experiences as an American soldier during the Vietnam War. In the chapter “The Man I Killed,” O’Brien opens the narrative with a grotesque description of a dead Vietcong guerrilla. The opening sentence catalogs the dead soldier’s wounds:

His jaw was in his throat, his upper lip and teeth were gone, his one eye was shut, his other eye was a star-shaped hole, his eyebrows were thin and arched like a woman's, his nose was undamaged, there was a slight tear at the lobe of one ear, his clean black hair was swept upward into a cowlick at the rear of the skull, his forehead was lightly freckled, his fingernails were clean, the skin at his left cheek was peeled back in three ragged strips, his right cheek was smooth and hairless, there was a butterfly on his chin, his neck was open to the spinal cord and the blood there was thick and shiny and it was this wound that had killed him.

The syntax is important here; this is a single sentence! O’Brien’s decision to format this gruesome list in this way mirrors the experience of the protagonist as he examines the corpse. Each minute detail washes over the young narrator and sears itself into his memory. This cascade of detail forces the reader to become a participant in the narrator’s guilt as if they are staring at the body alongside him.
O’Brien further evokes the narrator’s guilt through the invention of a backstory for the body who had been a living, breathing, feeling person mere moment before. Making inferences based on the body’s slight build, the narrator invents an elaborate backstory for his opponent. He imagines that the Vietnamese soldier had been an aspiring “mathematics scholar” who had laid in bed at night “wishing the Americans would go away.” This displays the narrator’s sensitivity and highlights his guilt. The image of O’Brien’s narrator staring at the body and imagining the life he had just ended packs a powerful emotional punch.
Tim O’Brien includes the gruesome list and the imaginary backstory in “The Man I Killed” because he hopes to communicate the horrible waves of conflicting emotions that accompany killing in war. Regardless of whether this story is factual, "The Man I Killed" captures the “story-truth” experience of thousands of young American soldiers in Vietnam.
I hope this helps!