Monopterus albus is one of the popular aquatic fish in Asia. Manual processing of eel cannot fully meet the large-scale production at present, due to the time-consuming, laborious, and low safety. In view of its slender and slimy body, an eel-cutting machine is required for the consumption of Monopterus albus. In this study, a miniature machine of automatic cutting was designed for the living Monopterus albus with a sticky surface. The machine consisted of conveying, clamping, and cutting parts. The double-clamped wheel to roller was used to capture the eel for transportation during cutting. The switch between laparotomy and back dissection was realized to change the feeding channel. The adaptive mechanism was equipped to meet the requirements of different sizes of eel cutting. Firstly, the geometry and weight parameters of Monopterus albus were measured using a straight ruler and precision electronic balance. The tribological parameters on the surface of Monopterus albus were measured by the inclined plane. The mechanical parameters of Monopterus albus meat were verified by compression test. Secondly, according to the rigid-flexible coupling principle, the rigid-damping model was equivalent to the contact between the Monopterus albus body and the clamping wheel and slide. The rigid-flexible coupling model was established by Abaqus and Adams simulation software. The analysis model was optimized to take the conveying time of the fish body, output speed, clamping force, and whole machine vibration as the test indexes in single-factor tests, such as the spring stiffness, slope Angle of the slide, and the speed of the clamping wheel. The results show that the clamping force first increased and then decreased with the increase of spring stiffness and the vibration amplitude of the whole machine decreased. But there was little influence on conveying time and output speed. The output time of the fish body decreased with the increase of slope angle, while the output speed, clamping force, and vibration of the whole machine increased. There was an increase in the conveying time of the fish body, the output speed, the clamping force, and the vibration of the whole machine, with the increase of the speed of the clamping wheel. The single- and multi-factor analyses were carried out to obtain the optimal working conditions. Specifically, the clamping wheel speed was 600 r/min, the spring stiffness was 1 200 N/m, and the slope angle was 16°. Finally, the processing experiment was performed on the automatic cutting machine for eel. There was consistency in the vibration amplitude range and the relationship between the three directions of the machine measuring points with the theoretical analysis. At the same time, the output speed of the fish body output machine was also measured to better agree with the theoretical analysis. The cutting of the machine under optimal working conditions has fully met the requirements. The correctness of the theoretical analysis was also verified by the test. The rigid-flexible coupling model can provide a strong reference to research and develop the subsequent equipment.