We present a precise and complete procedure for processing spectral data observed by the one-meter New Vacuum Solar Telescope (NVST). The procedure is suitable for both sit-and-stare and raster-scan spectra. In this work, the geometric distortions of the spectra are first corrected for subsequent processes. Then, considering the temporal changes and the remnants of spectral lines in the flat-field, the original flat-field matrix is split into four independent components to ensure a high-precision flat-fielding correction, consisting of the continuum gradient matrix, slit non-uniform matrix, CCD dust matrix, and interference fringe matrix. Subsequently, the spectral line drifts and intensity fluctuations of the science data are further corrected. After precise reduction with this procedure, the measuring accuracies of the Doppler velocities for different spectral lines and of the oscillation curves of the chromosphere and photosphere are measured. The results show that the highest measuring accuracy of the Doppler velocity is within 100 ms(-1), which indicates that the characteristics of the photosphere and chromosphere can be studied cospatially and cotemporally with the reduced spectra of the NVST.