In this study, a novel double-stage hydraulic system incorporating a hydraulic controllable accumulator (HCA) was proposed to simultaneously improve the energy and working efficiency of the hydraulic fineblanking press. Within this system, an innovative controller was proposed to orchestrate the HCA's operations, allowing it to adeptly adapt to abrupt pressure fluctuations and the energy demands from the external load. Within this study, a meticulous analysis was conducted to assess the energy demands of the fineblanking process and the function requirements of the hydraulic system. Subsequently, the energy consumption model based on the energy conservation law was established to analyze the supply-demand relationship of each stage and the energy conversion characteristic of capacitive energy, inertial energy, and resistive energy, thereby calculating these key parameters of the HCA. Then, an accurate simulation model was meticulously established and ultimately validated by the 1000-ton hydraulic fineblanking press, enabling a comprehensive assessment of the system's working performance and energy consumption characteristics. The simulation and experimental results showed that within this proposed system, the main cylinder circuit accounted for a big part of energy consumption, three times higher than that of the fast cylinder circuit. In the fast cylinder circuit, both resistive and capacitive energy were prominent, whereas in the main cylinder circuit, capacitive energy took precedence. Compared to the traditional system, the proposed system performed better with lower system pressure fluctuation and higher working efficiency increased by 10%. Moreover, the energy efficiency of the proposed system reached 45.9%, 20.35% higher than that of the traditional system, resulting in a reduction in energy consumption of 169.4 kJ per duty cycle.