A method to study the machine tool′s spatial cutting stability is proposed based on the Kriging model, for the complex and uncertain prediction of the cutting stability caused by the spatial pose change of machining point. Taking the minimum limit cutting depth as the research object, this method establishes a Kriging model to predict the relationships between the cutting stability and the machining position, revealing the spatial change rule of the minimum limit cutting depth. The improved particle swarm optimization is introduced to calculate the machining position with the optimal minimum limit cutting depth, which is also combined with the cutting experiment and the energy distribution theory to determine the modes easy to chatter and the related weak joints. Then, the joints stiffness is optimized to improve the minimum limit cutting depth further. The proposed cutting stability analysis method has been applied to a time-consuming process of a three-axis vertical machining center. The position changes show great effects on the machining stability, which are combined with the optimization scheme of the joint stiffness to improve the minimal cutting depth effectively.