With the aim of reducing the vibration and maximum stress of a cogged V-belt and determining the appropriate cogged V-belt for the vertical disc stump grinder (RG25HD), this paper analyses the relationship between, on the one hand, the horizontal displacement of the vibration and node stress and, on the other, the tooth profile and belt speed. In addition, the pattern of the vibration and node stress of the cogged V-belt is investigated using various tooth profiles and belt speeds. Our approach uses a rigid/flexible coupling simulation of belt power transmission based on a finite element flexible body method and employs Recurdyn multi-body dynamics software. After the simulation, we obtain the stress distribution of the belt, the lateral displacement curve and the node stress curve. Our results indicate that cog shape affects belt stress and vibration. When selecting or designing a cogged V-belt, a belt with trapezoidal cogs is preferable. Regarding the effect of belt speed, the trapezoidal cogged V-belt’s lateral vibrating displacement and maximal stress increase with an increase in belt speed. Therefore, when the stump grinder is in operation, its revolving speed should be maintained at a low rate to reduce vibration and prolong the belt’s life.