Salt stress is a common abiotic stress that negatively affects crop growth and yield. However, there have been significant differences found on the effect degree and management mechanism in plants under neutral salt stress and alkaline stress. In this study, two soybean cultivars, Heihe 49 (HH49, saline-alkali stress tolerant) and Henong 95 (HN95, saline-alkali stress sensitive), were hydroponically cultured and treated with salt solutions of 25, 50, and 75 mM Na+ in the form of NaCl, Na2SO4, NaHCO3, and Na2CO3. Plants treated with alkaline stress (NaHCO3 and Na2CO3) showed a greater decrease in root growth and root activity of both soybean cultivar seedlings than that under neutral salt stresses (NaCl and Na2SO4) with 25–75 mM Na+ concentration. Alkaline stress (25–50 mM Na+ content) activated a higher ability of antioxidant defense (by enhancing the activists of superoxide dismutase (SOD), peroxidase (POD), and ascorbate peroxidase (APX)) and increased the content of soluble sugars to a higher level than that under neutral salt stresses. However, 75 mM Na+ content salt treatments reduced antioxidant enzyme activities and osmotic regulating substance content. Furthermore, alkaline salt and neutral salt stress was able to induce DNA damage and cell cycle arrest in HH49 and HN95 seedling roots. Treatment with Na2CO3 induced the least random amplification polymorphic DNA (RAPD) polymorphism in soybean seedling roots among all salt treatments, which could have been related to the early cell cycle arrest.