“Sangre de Mi Sangre” is a film bent on desperation. As it follows the parallel journeys of two Mexican teenagers who smuggle themselves to New York, the film’s relentless focus on the adversities faced by illegal immigrants eventually tips from heartbreak to preachy pulp.

The film, the debut feature by Christopher Zalla, won a Grand Jury Prize at Sundance last year, a testament to the themes and performances at play. But the story itself tends too often toward cliché to sustain the drama set in motion.

“Sangre de Mi Sangre” tells the story of Juan (Armando Hernández), an orphaned teenage thief, and Pedro (Jorge Adrián Espíndola), a vulnerable 17-year-old, but it soon refracts into a display of the wide and varying ways that immigrants struggle against the obstacles of daily life and the ways they can be abused.

The film begins in Mexico, where we watch as Juan flees from some men with guns and lucks into a ride to New York. Among the other immigrants is young Pedro, who, illiterate and impossibly trusting, holds a letter from his mother and confides in his new friend that he is going to find his father, a wealthy restaurateur in Brooklyn. But when Pedro wakes up in New York, Juan is gone. And so are his belongings.

When Diego (Jesús Ochoa) opens his door to a young man claiming to be his son, it is actually Juan posing as Pedro, looking for a payload. But instead of a magnanimous man with a fat wallet, Juan meets a disgruntled dishwasher. As the two feel each other out and Diego tries to decipher if the boy is really his son, Pedro embarks on his own New York experience, getting hustled and abused on account of his trusting nature. One particular rip-off turns into a kind of friendship with Magda (Paola Mendoza), a hustler who seems to live on the streets for the fun of it. But troubles continue to plague the pair.

Mr. Zalla has created a world immune to the rule of law, where the consequences of daily occurrences are far from mundane. Each of the characters is forced to adapt and make do from a vulnerable position, where police protection is an unattainable luxury.

Suffering indignities while striving to get by seems to be par for the course. Diego stoically stashes the bulk of his earnings, but is openly mocked by his co-workers at the restaurant where he washes dishes. Magda finds a way to swindle most any situation, but she’s unable to avoid the inevitable perils of living on the street as a young woman. Pedro finds himself continually mistreated in this foreign place, but he quickly adapts to monetizing things he has that others want. And Juan scrapes by trying to make the most profit from the least amount of effort, constantly on the brink of losing control.

As the characters battle their unfortunate fates and struggle to retain some semblance of dignity, it seems as though things will not be working out for anyone in this story. Around every corner is another opportunity for degradation or violence. Whether through naiveté, a moment of lapsed vigilance, or extremely bad luck, each of the characters suffers a stack of setbacks that overwhelms the film.

From underpaying jobs to the American distrust of Spanish speakers and outright racism, Mr. Zalla spends time on so many of the minor and major insults that abound in immigrant life that he effectively strips the momentum from the story.

Mr. Ochoa leads the cast with his formidable depiction of Diego as a brooding but sympathetic loner. Diego is relentlessly endearing, even though his barely contained rage never gets the attention it seems to demand. Ms. Mendoza makes a startling image on-screen, but she never really manages to break out of cinematic cliché. Likewise, Mr. Espíndola is confined to a deer-in-the-headlights existence as Pedro, but he manages to let a wounded wholesomeness shine through, while Mr. Hernández’s dead-eyed portrayal of Juan leaves a chill on the screen.

As Juan gains Diego’s trust, and Pedro feels his way on the streets by himself, “Sangre de Mi Sangre” shifts from a moving immigrant tale to moralist pulp. No one can dispute the difficulty of living in a place where the law is more of an inconvenience than a protective guide, but a point exists at which a cinematic commitment to pessimism becomes just as manufactured as a happy ending.