A typical white-matter integrity and elevated dopamine levels have been reported for individuals who stutter. We investigated how such abnormalities may lead to speech dysfluencies due to their effects on a syllable-sequencing circuit that consists of basal ganglia (BG), thalamus, and left ventral premotor cortex (vPMC). “Neurally impaired” versions of the neurocomputational speech production model GODIVA were utilized to test two hypotheses: (1) that white-matter abnormalities disturb the circuit via corticostriatal projections carrying copies of executed motor commands, and (2) that dopaminergic abnormalities disturb the circuit via the striatum. Simulation results support both hypotheses: in both scenarios, the neural abnormalities delay readout of the next syllable’s motor program, leading to dysfluency. The results also account for brain imaging findings during dysfluent speech. It is concluded that each of the two abnormality types can cause stuttering moments, probably by affecting the same BG-thalamus-vPMC circuit.