Compared with traditional deepwater drilling, riserless mud recovery (RMR) drilling technology has the advantages of improving drilling efficiency, reducing risks, and minimizing environmental effects. Therefore, RMR drilling technology has been widely applied in recent years. This study primarily investigates the relationships among reverse torque, vibration, and input parameters of mud pumps in riserless mud recovery drilling. Firstly, the operating principle and the structure of the mud pump module are analyzed, and an analytical model for the reverse torque and the vibration of the mud pump is established. Secondly, relevant data are derived from theoretical calculations and experiments, and the relationships among the reverse torque, vibration, and input parameters of the mud pump are analyzed using ANSYS (Version 2020 R1) software. Furthermore, the SVR (support vector regression) algorithm is employed to predict and analyze the amplitude of the mud pump’s vibration. Finally, the conclusions are drawn based on the findings of the relationships among the reverse torque, vibration, and input parameters of the mud pump. The findings show that the reverse torque of the mud pump increases approximately linearly with an increase in rotational speed, and the vibration of the mud pump increases and then decreases with an increase in rotational speed. The predicted values obtained through the prediction algorithm closely match the actual values. The findings provide a valuable reference for the application of RMR technology.