Tove, a troubled young woman, is contemplating suicide when she meets Jesse, a carefree vagabond. She agrees to remain in his company on one condition: he must help her find heroin.

"Suicide Tuesday" opens to a scene of Tove, a troubled young woman, standing on the precipice of a cliff, contemplating suicide. There she unexpectedly crosses paths with Jesse, a carefree vagabond who tries to help her, despite her resistance. She agrees to remain in his company on one condition: he must help her find heroin. Jesse agrees, secretly planning to dissuade her from her course. On their journey together, they discover a shared sense of alienation, and Tove gradually lets Jesse into her heart. As the story unfolds, Tove's traumatic experiences that pushed her into this abyss are brought to light.