The performance of biomimetic underwater vehicles directly depends on the correct design of their propulsion system and its control. These vehicles can attain highly efficient motion, hovering and thrust by properly moving part(s) of their bodies. In this article, a mathematical modeling and waypoint guidance system for a biomimetic autonomous underwater vehicle (BAUV) is proposed. The BAUV achieves sideways and dorsoventral thunniform motion by flapping its caudal fin through a parallel mechanism. Also, an analysis of the vehicle’s design is presented. A thrust analysis was performed based on the novel propulsion system. Furthermore, the vehicle’s kinematics and dynamic models were derived, where hydrodynamic equations were obtained as well. Computed models were validated using simulations where thrust and moment analysis was employed to visualize the vehicle’s performance while swimming. For the path tracking scheme, a waypoint guidance system was designed to correct the vehicle’s direction toward several positions in space. To accurately obtain waypoints, correction over the propeller’s flapping frequency and bias was employed to achieve proper thrust and orientation of the vehicle. The results from numerical simulations showed how by incorporating this novel propulsion strategy, the BAUV improved its performance when diving and maneuvering based on the dorsoventral and/or sideways configuration of its swimming mode. Furthermore, by designing proper strategies to regulate the flapping performance of its caudal fin, the BAUV followed the desired trajectories. The efficiency for the designed strategy was obtained by comparing the vehicle’s traveled distance and ideal scenarios of straight-line trajectories between targets. During simulations, the designed guidance system presented an efficiency of above 80% for navigation tasks.