With the substantial increase of the FMCW radars used for autonomous driving and other applications in the area of surveillance, mutual interference has become a major concern. Recently, Deep Learning (DL) models have been used in FMCW radar interference mitigation with great success, but no research has been conducted in processing the time-frequency (t-f) maps of acquired beat signals. Considering the different distributions of useful beat signals and interferences in the t-f domain, a fully convolutional network (FCN) is proposed to suppress the interference and noise in the t-f spectrum obtained by the short-time Fourier transform (STFT) algorithm. The experimental results on the simulated radar signals show that the proposed FCN provides superior interference suppression with few parameters. Moreover, the qualitative results on the measured radar signals collected in real-world scenarios emphasize the excellent generalization capacity of the model. Finally, we show that our proposed approach achieves the best performance compared to state-of-the-art techniques.