The jumping motion of legged robots is an effective way to overcome obstacles in the rugged microgravity planetary exploration environment. At the same time, a quadruped robot with a manipulator can achieve operational tasks during movement, which is more practical. However, the additional manipulator will restrict the jumping ability of the quadruped robot due to the increase in the weight of the system, and more active degrees of freedom will increase the control complexity. To improve the jumping height of a quadruped robot with a manipulator, a bio-inspired take-off maneuver based on the coordination of upper and lower limbs is proposed in this paper. The kinetic energy and potential energy of the system are increased by driving the manipulator-end (ME) to swing upward, and the torso driven by the legs will delay reaching the required peak speed due to the additional load caused by the accelerated ME. When the acceleration of ME is less than zero, it will pull the body upward, which reduces the peak power of the leg joints. Therefore, the jumping ability of the system is improved. To realize continuous and stable jumping, a control framework based on whole-body control was established, in which the quadruped robot with a manipulator was a simplified floating seven-link model, and the hierarchical optimization was used to solve the target joint torques. This method greatly simplifies the dynamic model and is convenient for calculation. Finally, the jumping simulations in different gravity environments and a 15° slope were performed. The jump heights have all been improved after adding the arm swing, which verified the superiority of the bio-inspired take-off maneuver proposed in this paper. Furthermore, the stability of the jumping control method was testified by the continuous and stable jumping.