We present a spectroscopic redshift catalog from the LAMOST Complete Spectroscopic Survey of Pointing Area (LaCoSSPAr) in the Southern Galactic Cap (SGC), which is designed to observe all sources (Galactic and extragalactic) by using repeating observations with a limiting magnitude of r=18.1mag in two 20deg^2^ fields. The project is mainly focusing on the completeness of LAMOST ExtraGAlactic Surveys (LEGAS) in the SGC, the deficiencies of source selection methods, and the basic performance parameters of the LAMOST telescope. In both fields, more than 95% of galaxies have been observed. A post-processing has been applied to the LAMOST 1D spectrum to remove the majority of remaining sky background residuals. More than 10000 spectra have been visually inspected to measure the redshift by using combinations of different emission/absorption features with an uncertainty of {sigma}_z_/(1+z)<0.001. In total, 1528 redshifts (623 absorption and 905 emission line galaxies) in Field A and 1570 redshifts (569 absorption and 1001 emission line galaxies) in Field B have been measured. The results show that it is possible to derive redshift from low S/N galaxies with our post-processing and visual inspection. Our analysis also indicates that up to one-fourth of the input targets for a typical extragalactic spectroscopic survey might be unreliable. The multi-wavelength data analysis shows that the majority of mid-infrared-detected absorption (91.3%) and emission line galaxies (93.3%) can be well separated by an empirical criterion of W2-W3=2.4. Meanwhile, a fainter sequence paralleled to the main population of galaxies has been witnessed both in Mr/W2-W3 and M*/W2-W3 diagrams, which could be the population of luminous dwarf galaxies but contaminated by the edge-on/highly inclined galaxies (~30%).