<p>Cutting conditions play critical roles in machining quality. Improper cutting conditions can cause chatter in unstable cutting, or result in large surface roughness even under stable cutting. The means of stability lobe diagram (SLD) and surface location error (SLE) are used in selecting the optimal cutting conditions, achieving a smooth machined surface. This paper proposes a novel scheme that applies the minimal realization to the existing semi-discretization methods to improve computational efficiency. The semi-discretization is applied separately to both the mechanical system and the cutting dynamics, and the two are then combined, after lifting, to form the closed-loop discrete map, in which unnecessary states are excluded and the monodromy matrix is minimized. This significantly reduces the computational complexity in the SLD analysis and enables an efficient calculation to the SLE prediction. Comparative results and verifications reveal the superior efficiency of the proposed scheme in both SLD and SLE predictions, comparing with the existing schemes.</p>