Seismic data acquired in the presence of mechanical vibrations or power facilities may be contaminated by strong interferences, significantly decreasing the data signal-to-noise ratio (S/N). Conventional methods, such as the notch filter and time-frequency transform method, are usually inadequate for suppressing non-stationary interference noises, and may distort effective signals if overprocessing. In this study, we propose a method for eliminating mechanical vibration interferences in seismic data. In our method, we extended the variational mode extraction (VME) technique to a multivariate form, called multivariate variational mode extraction (MVME), for synchronous analysis of multitrace seismic data. The interference frequencies are determined via synchrosqueezing-based time-frequency analysis of process recordings; their corresponding modes are extracted and removed from seismic data using MVME with optimal balancing factors. We used synthetic data to investigate the effectiveness of the method and the influence of tuning parameters on processing results, and then applied the method to field datasets. The results have demonstrated that, compared with the conventional methods, the proposed method could effectively suppress the mechanical vibration interferences, improve the S/Ns and enhance polarization analysis of seismic signals.