In this study, a vector propulsion mechanism with the UPR-UPU-UR configuration was investigated to develop an underwater vehicle propulsion device with space attitude adjustment, high precision, and large torque power transmission. First, the degree of freedom of the vector propulsion mechanism was calculated using screw theory, and the position model of the vector propulsion mechanism was constructed using an analytical method. Second, the relationship between the output vector and input vectors of the vector propulsion mechanism was derived, and the particle swarm optimization algorithm was used to calculate the position positive solution of the vector propulsion mechanism. Third, the singularity of the mechanism was evaluated using the Jacobian matrix corresponding to the angle of velocity and the characteristics of the mechanism, and the workspace of the vector propulsion mechanism was calculated. Finally, the experimental platform of the vector propulsion mechanism with the UPR-UPU-UR configuration was built, and experiments were conducted. The results of numerical simulations and experiments demonstrate that the precise position and attitude of the mechanism could be obtained when the absolute error was less than 0.001°, and the maximum error between the experimental and theoretical values of the vector propulsive performance was 5%, which proved that the mechanism had good motion characteristics and propulsive performance. The vector propulsion mechanism adjusted the thrust direction of the propeller by varying the length of two branch chains, such that the robot could exhibit various motion modes, such as yaw, pitch, and roll, which helped in achieving the complex underwater motion.