Recognition of DNA base mismatches and their subsequent repair by enzymes is vital for genomic stability. However, it is difficult to comprehend such a process in which enzymes sense and repair different types of mismatches with different ability. It has been suggested that the differential structural changes of mismatched bases act as cues to the repair enzymes, although the effect of such DNA structural changes on surrounding water and ion dynamics is inevitable due to strong electrostatic coupling among them. Thus, collective dynamics of DNA, water, and ions near the mismatch site is believed to be important for mismatch recognition and repair mechanism. Here we show that introduction of a T.T mismatch in the minor groove of DNA induces dispersed (collective) power-law solvation dynamics (of exponent similar to 0.24), measured by monitoring the time-resolved fluorescence Stokes shifts (TRFSS) of two popular minor groove binders (Hoechst 33258 and DAPI) over five decades of time from 100 fs to 10 ns. The same ligands however sense different dynamics (power-law of exponent similar to 0.15 or power-law multiplied with biexponential relaxation) in the minor groove of normal-DNA. The similar fluorescence anisotropy decays of ligands measured in normal- and T.T-DNA suggest that Stokes shift dynamics and their changes in T.T-DNA purely originate from the solvation process, and not from any internal rotational motion of probe-ligands. The dispersed power-law solvation dynamics seen in T.T-DNA indicate that the ligands do not sense any particular (exponential) relaxation specific to T.T wobbling and/or other conformational changes. This could be the reason why T.T mismatch is recognized by enzymes with lower efficiency compared to purine-pyrimidine and purine-purine mismatches.