A highly accurate digital-twin spiral bevel gear or hypoid gear is often required for dynamic analysis or stress analysis for gear transmission. However, a highly accurate digital-twin solid model is not always available because the final hypoid gear is completed by the gear manufacturer. This study constructs a digital-twin from a sample hypoid gear. The tooth surface of sample gear is digitized as topographical grids using a coordinate measuring machine (CMM) or a gear measurement center. The geometric parameters (the surface position vector, the normal vector, the principal curvatures, and the corresponding principal directions) for the measured tooth surface (MTS) are then extracted using numerical differential geometry (NDG). The machine settings and the cutter parameters for the sample hypoid gear are obtained by minimizing the topographical error between the replicated digital-twin and the sample gear using optimization software. The initial estimation for the machine settings and the cutter parameters is calculated using an explicit form of the modified-roll motion (MRM), which decreases numerical divergence and time that is required for calculation. The machine settings, the cutting tool parameters, and the auxiliary flank modification (AFM) motion are used as the design variables. A numerical example is presented to verify the proposed methodology. The numerical results show that the replicated digital-twin that is developed using the proposed method is sufficiently accurate for industrial applications.