In this paper, we propose a novel method for frequency modulated continuous wave (FMCW) radar mutual interference mitigation based on the discrete fractional Fourier transform (DFrFT). Interference chirps are detected and mitigated by compression and zeroing in the fractional domain. We provide an efficient implementation that can deal with multiple interferers, where we perform consecutive DFrFTs utilizing its angle-additivity property. For that purpose, we generalize and reduce the computational complexity of the multi-angle centered discrete fractional Fourier transform [1]. Our algorithm is designed to be simple and fast such that it can be implemented in hardware. We evaluate our algorithm on a synthetic I/Q-modulated dataset and outperform reference methods in terms of the mean squared error, signal-to-interference-plus-noise ratio, error vector magnitude, true positive rate, false alarm rate and F1-score.