Recovering the protein activity of p53 mutants through small molecule ligand binding (eg. arsenic) is an important strategy for tumor suppressor therapy. However, the mechanistic basis on the changes of collective dynamics and their roles of p53 protein in functional recovery process has not been fully elucidated. Herein, the normal mode calculations based on all-atom elastic network model are employed to characterize the terahertz low frequency motions of core DNA-binding domain (p53C) which is essential for p53 protein activities in transcriptional transactivation. We find that the lowest-frequency collective vibration mode of the p53C mutant is effectively restored by the binding of arsenic (III) ligand. In R249S mutant, the L1 loop is stabilized through restricting the swing-out movement. The results obtained from atomic backbone fluctuations suggest that the arsenic binding can significantly improve the L1 loop and L2 loop fluctuations. The statistical analysis of low frequency vibration mode reflects that the arsenic-bound R249S mutant has an apparent recovery of frequency shift in the terahertz range. The residue-residue motion correlation also suggests that structural components binding to arsenic are dynamically coupled. In the H2 helix with arsenic-binding residues, the motions of C124, C135, M133 and C141, are correlated with the arsenic recovery. These results provide the terahertz biophysical mechanism for the recovery effect of arsenic (III) on the p53 protein activity and new evidence for the coupling of the low-frequency vibration characteristics of protein structures with its function, thus giving a new physical insight into the p53 related cancer therapies.