This paper first presents a system concept of a hydrostatically driven hydraulic excavator. In this system, pumps and actuators are connected each other. Then, the speed of actuators is controlled by the pump flow rate. Herein, a hydraulic excavator has 7 actuators and 4 pumps, and connection/disconnection of each pump and actuator are controlled by 3x4 directional control valves. Microcomputers execute the following controls : maximum pressure limiting (pressure cutoff control), pump absorption power control for prevention of engine stop and suitable power distribution to pumps, transient vibration damping, maximum acceleration limiting and resolved motion rate control of the excavator's arm. Furthermere, in this paper, we report the experimental study of pressure cutoff control which is a basic function for energy saving in a hydrostatically driven hydraulic excavator.