A kinetic study is reported for the SNAr reaction of 1-Y-substituted-phenoxy-2,4-dinitrobenzenes (1a-1h) with OH- in 80 mol % $H_2O$/20 mol % DMSO at $25.0{pm}0.1^{circ}C$. The second-order rate constant ($k_{OH^-}$) increases as the substituent Y in the leaving group changes from an electron-donating group (EDG) to an electronwithdrawing group (EWG). The Br${o}$nsted-type plot for the reactions of 1a-1h is linear with ${eta}_{lg}$ = -0.16, indicating that the reactivity of substrates 1a-1h is little affected by the leaving-group basicity. A linear Br${o}$nsted-type plot with ${eta}_{lg}=-0.3{pm}0.1$ is typical for reactions reported previously to proceed through a stepwise mechanism in which formation of a Meisenheimer complex is the rate-determining step (RDS). The Hammett plot correlated with ${sigma}_Y{^{circ}}$ constants results in a much better correlation than that correlated with ${sigma}_Y{^-}$constants, implyng that no negative charge is developing on the O atom of the leaving group (or expulsion of the leaving group is not advanced at all in the TS). This excludes a possibility that the $S_NAr$ reaction of 1a-1h with $OH^-$ proceeds through a concerted mechanism or via a stepwise pathway with expulsion of the leaving group being the RDS. Thus, the current reactions have been concluded to proceed through a stepwise mechanism in which expulsion of the leaving group occurs rapidly after the RDS.