The robotic machining is one of the most versatile manufacturing technologies. Its emerging helped to reduce the machining cost of complex parts. However, its application is sometimes limited due to the low rigidity of the robot. This low stiffness leads to high level of vibrations that limit the quality and the precision of the machined parts. In the present study, the vibration response of a robotic machining system was investigated. To do so, a new method based on the variation of spindle speed was introduced for machining operation and a new process stability criterion (CS) based on acceleration energy distribution and force signal was proposed for analysis. With the proposed method the vibrations and the cutting force signals were collected and analyzed to find a reliable dynamic stability machining domain. The proposed criterion and method were validated using data obtained during high speed robotic machining of 7075-T6 blocks. It was found that the ratio of the periodic energy on the total energy (either vibrations or cutting forces) is a good indicator for defining the degree of stability of the machining process. Besides, it was observed that the spindle speed with the highest ratio stability criterion is the one that has the highest probability to generate the best surface finish. The proposed method is rapid and permits to avoid trial-error tests during robot programming.