This paper investigates the mathematical modeling and dynamic analysis of a turning tool equipped with a rod-and-spring damping element using the coherence function. Vibrations (chatter) occurring during turning operations adversely affect surface quality, tool life, and process stability. The “machine tool–tool–workpiece” system is represented as a singledegree-of-freedom time-delay dynamic model, considering the effect of the damping element on the overall damping coefficient. Numerical simulations are carried out in the MATLAB environment, and the results are analyzed using vibration amplitude, frequency spectra, and coherence function. The obtained results demonstrate the effectiveness of the damped turning tool in reducing vibrations and confirm that the coherence function is a powerful tool for evaluating the causal relationship between cutting forces and vibration responses.