We present results of a 1.1 mm deep survey of the AKARI Deep Field South (ADF-S) with AzTEC mounted on the Atacama Submillimetre Telescope Experiment (ASTE). We obtained a map of 0.25 deg2 area with an rms noise level of 0.32–0.71 mJy. This is one of the deepest and widest maps thus far at millimetre and submillimetre wavelengths. We uncovered 198 sources with a significance of 3.5–15.6σ, providing the largest catalog of 1.1 mm sources in a contiguous region. Most of the sources are not detected in the far-infrared bands of the AKARI satellite, suggesting that they are mostly at z ≥ 1.5 given the detection limits. We construct differential and cumulative number counts of the ADF-S, the Subaru/XMM Newton Deep Field (SXDF), and the SSA 22 field surveyed by AzTEC/ASTE, which provide currently the tightest constraints on the faint end. The integration of the differential number counts of the ADF-S find that the contribution of 1.1 mm sources with  ≥1 mJy to the cosmic infrared background (CIB) at 1.1 mm is 12–16%, suggesting that the large fraction of the CIB originates from faint sources of which number counts are not yet constrained. We estimate the cosmic star-formation rate density contributed by 1.1 mm sources with  ≥1 mJy using the differential number counts and find that it is lower by about a factor of 5–10 compared to those derived from UV/optically-selected galaxies at z ~ 2–3. Clustering analyses of AzTEC sources in the ADF-S and the SXDF find that bright (>3 mJy) AzTEC sources are more strongly clustered than faint (< 3 mJy) AzTEC sources and the average mass of dark halos hosting bright AzTEC sources was calculated to be 1013–1014M⊙. Comparison of correlation length of AzTEC sources with other populations and with a bias evolution model suggests that dark halos hosting bright AzTEC sources evolve into systems of clusters at present universe and the AzTEC sources residing the dark halos evolve into massive elliptical galaxies located in the center of clusters.