Equipped with one degree of freedom in one-dimensional translation of the base, a mobile dual-arm robot (MDAR) is proposed in this paper, and the two arms and the base move simultaneously. As a result, the motion of the base has a significant influence on the motion of both end-effectors at the same time, and the relative positions of the two end-effectors change all the time. Therefore, this paper focuses on the main issues related to the presented MDAR in two key areas: the relative dynamics and relative force/position hybrid control. First, based on the D-H parametric method, the relative kinematics of the proposed MDAR is established, and the relative Jacobian matrix of the robot is derived. Secondly, the dynamic model of the proposed MDAR is constructed using the Lagrangian method. Furthermore, a closed-loop control strategy for relative force/position hybrid control of the MDAR based on the relative dynamics is proposed to enable the two end-effectors of the MDAR to track the planned trajectory accurately. Finally, a simulation is carried out on a dual-arm cutting robot (DACR) for a coal mine to prove the effectiveness of the proposed relative dynamics and the proposed relative force/position hybrid control law in terms of the absolute error (AE) and root mean square error (RMSE). The results show that the proposed relative dynamic model and relative force/position hybrid control can significantly reduce error of the DACR, effectively improve the adaptability and operation accuracy of the system to complex environment, and verify the feasibility and superiority of the method in practical application.