With increasing application of frequency-modulated continuous wave (FMCW) radars in autonomous vehicles, mutual interference among FMCW radars poses a serious threat. Through this paper, we present a novel approach to effectively and elegantly suppress mutual interference in FMCW radars. We first decompose the received signal into modes using variational mode decomposition (VMD) and perform time-frequency analysis using Fourier synchrosqueezed transform (FSST). The interference-suppressed signal is then reconstructed by applying a proposed energy-entropy-based thresholding operation on the time-frequency spectra of VMD modes. The effectiveness of proposed method is measured in terms of signal-to-interference plus noise ratio (SINR) and correlation coefficient for both simulated and experimental automotive radar data in the presence of FMCW interference. Compared to other existing literature, our proposed method demonstrates significant improvement in the output SINR by at least 14.07 dB for simulated data and 9.87 dB for experimental data.