In this paper, a novel two-stage dish concentrator (TSD) with a rotary secondary mirror (SM) is presented for solar thermal water/CO2 splitting. An in-house code for ray-tracing simulation of the concentrator was developed and validated. Among all feasible geometries, a hyperboloid with an upper sheet is the most popular option and is widely used as a secondary reflector, which is mainly discussed here. All para-hyperboloid geometric combinations can be categorized into three typical patterns (φ1 < π/2, φ1 = π/2, φ1 > π/2, φ1 = field angle of PM). The initial designs of the TSD, respective to different off-axis levels for each combination, were first designed. Then a new mathematical model was introduced to reshape the SM to reach optimal truncated designs. Finally, a new concept of an off-axis primary mirror (PM) combined with the truncated SM was evaluated by using the in-house ray-tracing code. The results include the optical efficiency, concentration ratio and intercepted radiant flux. The best solutions with the highest optical efficiency fall in the range π/2 ≤ φ1 ≤ (π − arcsin 0.8) rads and 0.4 ≤ NA2 ≤ 0.6 (NA2 = sin φ2, φ2 = field angle of SM), which vary with the concentration ratio and inclination angle.