SEOUL—North Korea’s cyberarmy has splintered into multiple groups and is unleashing orchestrated attacks increasingly focused on funneling stolen funds to the secretive nation, according to a government-backed South Korean report released Thursday.

The emphasis on finances represents a significant shift from Pyongyang’s prior patterns of attack seeking to obtain military information, destabilize networks or intimidate. It also shows how North Korea’s fast-evolving—but costly—nuclear-missile program has accelerated its need...