Second-order rate constants ($k_N$) have been measured for nucleophilic substitution reactions of S-4-nitrophenyl thiobenzoate with a series of alicyclic secondary amines in $H_2O$ containing 20 mol % DMSO at 25.0 ${pm}$ 0.1 ${^{circ}C}$. The Br$phi$nsted-type plot exhibits a downward curvature, i.e., $eta_{nuc}$ decreases from 0.94 to 0.34 as the amine basicity increases. The reactions in the aqueous DMSO have also been suggested to proceed through a zwitterionic tetrahedral intermediate (T${pm}$) with change in the RDS on the basis of the curved Br$phi$nsted-type plot. The reactions in the aqueous DMSO exhibit larger $k_N$ values than those in the aqueous EtOH. The macroscopic rate constants ($k_N$) for the reactions in the two solvent systems have been dissected into the microscopic rate constants ($k_1;and;k_2/k_{-1}$ ratio) to investigate effect of medium on reactivity in the microscopic level. It has been found that the $k_2/k_{-1}$ ratios are similar for the reactions in the two solvent systems, while $k_1$ values are larger for the reactions in 20 mol % DMSO than for those in 44 wt % EtOH, indicating that the larger $k_1$ is mainly responsible for the larger $k_N$. It has been suggested that the transition state is more stabilized in 20 mol % DMSO through mutual polarizability interaction than in 44 wt % EtOH through H-bonding interaction.