Stereopsis provides critical information for the spatial visual perception of object form and motion. We used virtual reality as a tool to understand the role of global stereopsis in the visual perception of self-motion and spatial presence using virtual environments experienced through head-mounted displays (HMDs). Participants viewed radially expanding optic flow simulating different speeds of self-motion in depth, which generated the illusion of self-motion in depth (i.e., linear vection). Displays were viewed with the head either stationary (passive radial flow) or laterally swaying to the beat of a metronome (active conditions). Multisensory conflict was imposed in active conditions by presenting displays that either: (i) compensated for head movement (active compensation condition), or (ii) presented pure radial flow with no compensation during head movement (active no compensation condition). In Experiment 1, impairing stereopsis by anisometropic suppression in healthy participants generated declines in reported vection strength, spatial presence and severity of cybersickness. In Experiment 2, vection and presence ratings were compared between participants with and without clinically-defined global stereopsis. Participants without global stereopsis generated impaired vection and presence similarly to those found in Experiment 1 by subjects with induced stereopsis impairment. We find that reducing global stereopsis can have benefits of reducing cybersickness, but has adverse effects on aspects of self-motion perception in HMD VR.