Fatigue loads associated with torsional and blade-edgewise vibrations are recognized as major reasons of large scale wind turbine failures. This paper presents an active mitigating control approach to reduce torsional and edgewise vibrations in the PMSG-based wind turbine. Due to the interactions of both vibrations, the active control is designed based on the expanded dynamic model of the mechanical-structural flexibilities. In this way, the blades are modeled as flexible cantilever beams, and thus, in the drive-train model the dynamics of the blades are considered. The control input to suppress the vibrations is achieved by the power electronic converters through adding an axillary term proportional to the speed difference between the blade and hub into the power control loop. This term manipulates the generator torque to counteract the unwanted vibrations. The needed drive-train and mechanical variables for making the auxiliary term are estimated by a novel robust method based on the sliding-mode observer. Using mathematical analyses and simulation results, it is shown that the proposed active mitigating approach well alleviates the fatigue loads of the torsional and edgewise modes even under severe changes in the drive-train stiffness coefficients. Thus, the proposed sensorless control approach is an appropriate remedy action for alleviation of WT fatigue loads even under parameters uncertainties.