Human brain organoids provide unique platforms for modeling development and diseases by recapitulating the architecture of the embryonic brain. However, current organoid methods are limited by interior hypoxia and cell death due to insufficient surface diffusion, preventing generation of architecture resembling late developmental stages. Here, we report the sliced neocortical organoid (SNO) system, which bypasses the diffusion limit to prevent cell death over long-term cultures. This method leads to sustained neurogenesis and formation of an expanded cortical plate that establishes distinct upper and deep cortical layers for neurons and astrocytes, resembling the third trimester embryonic human neocortex. Using the SNO system, we further identify a critical role of WNT/β-catenin signaling in regulating human cortical neuron subtype fate specification, which is disrupted by a psychiatric-disorder-associated genetic mutation in patient induced pluripotent stem cell (iPSC)-derived SNOs. These results demonstrate the utility of SNOs for investigating previously inaccessible human-specific, late-stage cortical development and disease-relevant mechanisms. Display omitted •SNOs maintain growth and laminar expansion over long-term culture•SNOs exhibit separated upper and deep cortical layers•Layer-specific WNT/β-catenin signaling regulates neuronal fate specification•DISC1 mutation causes deficits in cortical neuron fate specification Cortical organoids can be used to model human brain development and disorders. Ming and colleagues overcome the diffusion limit using a slicing method to prevent interior cell death and sustain organoid growth over long-term culture. The resulting organoids recapitulate late-stage human cortical developmental features, including formation of distinct cortical layers.