The method of using millimeter-wave radar sensors to detect human vital signs, namely respiration and heart rate, has received widespread attention in non-contact monitoring. These sensors are compact, lightweight, and able to sense and detect various scenarios. However, it still faces serious problems of noisy interference in hardware, which leads to a low signal-to-noise ratio (SNR). We used a frequency-modulated continuous wave (FMCW) radar sensor operating at 77 GHz in an office environment to extract the respiration and heart rate of a person accustomed to sitting in a chair. Indeed, the proposed signal processing includes novel impulse denoising operations and the spectral estimation decision method, which are unique in terms of noise reduction and accuracy improvement. In addition, the proposed method provides high-quality, repeatable respiration and heart rates with relative errors of 1.33% and 1.96% on average compared with the reference values measured by a reliable smart bracelet.