Root cutting is an important process in garlic field harvesting but is the weakest link in the full mechanization of garlic production. To improve the current situation of technological backwardness and poor operational quality of mechanized garlic root-cutting in the main garlic-producing regions of China, this study combined the physical characteristics and agronomic requirements of garlic plants, and proposed an innovative floating root-cutting technology for garlic combine harvesters that enables the top alignment of bulb, adaptive profiling floating of cutter, and embedded cutting of roots. Through the kinematic analysis of the floating cutting process, the coordinate equations of the initial contact point of the bulb, the mathematical model of the floating displacement of the cutting component. Using computer simulation techniques, the dynamic simulation study of the floating cutting process was carried out in the rigid-flexible coupling numerical simulation model of root-cutting mechanism and garlic plant. The influence law of garlic conveying speed, extension spring preload force and stiffness on the floating displacement of the cutting component and the angular velocity of swing arm reset and its formation causes were analyzed by a single-factor simulation test. The key operating parameters of the root-cutting mechanism were optimized through the computerized virtual orthogonal test and fuzzy comprehensive evaluation. The significance of the factors affecting the floating cutting performance decreased in the following order: extension spring preload force, garlic conveying speed and extension spring stiffness. The optimal parameter combination of the root cutting mechanism obtained from the optimization were as follow: extension spring preload force was 16 N, garlic conveying speed was 0.8 m/s, and extension spring stiffness was 215 N/m. Tests conducted with the optimal parameter combination yielded a root excision rate of 92.72%, which meets the requirements of Chinese garlic field harvesting quality. This study provides computer simulation optimization methods for the optimal design of the root-cutting mechanism, and also provides technical and equipment support for the full mechanization of garlic production in China.