BRASILIA—A gang fight in a prison in Brazil’s Para state left at least 57 dead, many by decapitation or asphyxiation, adding to a string of gruesome clashes in the country’s overloaded prison system as the government struggles to fight rampant crime.

The violence started at around 7 a.m. Monday when members of one of the prison’s two leading gangs broke into a shipping container modified to hold members of a rival gang. The attackers beheaded 16 of their enemies before setting the place on fire, officials said. The fire spread,...