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Faster-than-Nyquist (FTN) signaling can improve spectral efficiency and enable high-speed transmission for next-generation communication systems. One of the most significant challenges in FTN transmission is how to remove the inter-symbol interference (ISI). In this paper, we propose a novel decision-directed successive interference cancellation (DDSIC) based on frequency-domain minimum-mean-square-error (MMSE) equalization for practical FTN systems. To reduce the computational complexity, the detection process is performed frame-by-frame in the frequency domain. In addition, we derive the theoretical bit error rate (BER) expression for each iteration in DDSIC as well as the BER lower bound for <inline-formula> <tex-math notation="LaTeX">M </tex-math></inline-formula>-ary quadrature amplitude modulated FTN systems. The simulation results verify the theoretical analyses and demonstrate that our proposed method enables lower complexity and better performance compared with state-of-the-art methods.