Machining vibrations are an important issue as they occur in all types of machining processes. Due to its negative impact on machining results, this phenomenon is undesirable, and so there have been continuous efforts to find solutions that will minimise it, and thus improve the stability and safety of the machining process. The paper attempts to determine the impact of toolholder type and cutting condition on the vibrations generated while milling an AZ31 magnesium alloy. The tests were performed using the three most common types of toolholders: ER, Shrink Fit and hydraulic. The vibration displacement and acceleration signals were analysed based on parameters such as Peak-to-Peak, Peak, and Root Mean Square. Composite Multiscale Entropy was also applied to check the stability of cutting processes and define the level of signal irregularity. To determine the frequencies of vibrations and to detect chatter vibrations Fast Fourier Transform was performed. This provides information on the stability and enables vibrations to be minimized by avoiding unfavourable cutting conditions.