This paper presents a novel model-free adaptive sliding mode control (MFA-SMC) algorithm, which is employed to actively adjust the amplitude and frequency of spindle speed variation (SSV) for chatter suppression in turning. The SSV technique is effective for mitigating regenerative chatter, which however is not widely applied due to its poor adaptability to time-varying characteristics of machining dynamics and cutting conditions. The online adjustment of SSV parameters has been reported in previous works, whereas the proportional integral differential (PID)-type controller used cannot compensate for the interactions when abruptly changing the reference input and the parameter tuning procedure consumes much time. The proposed method integrates the model-free adaptive control (MFAC) with the global sliding mode control (GSMC). The method is data-driven and only dependent on the measured input/output data of the cutting process in this paper, which are the normalized wavelet packet entropy and SSV parameters, respectively. The bounded-input bounded-output stability and the tracking error convergence of the proposed control algorithm are guaranteed by theoretical analysis. The effectiveness of the proposed chatter suppression method is investigated with numerical simulations. Finally, experimental results demonstrate that chatter vibration under different cutting conditions can be effectively mitigated by the proposed method.