Saponite clay belongs to the phyllosilicate family and is comprised of layers of Si(IV) tetrahedra and Al(III) or Mg(II) octahedra with definite interlayer spacing. In these systems, the trivalent ion substitutions in the tetrahedral layers lead to negative charge on the layers. Here we report the dynamics of water contained in [Si(6.97)Al(1.03)][Ni(6.00)]O(20)(OH)(4)[Na(1.03)]·28H(2)O (SAP-1) and [Si(7.13)Fe(0.86)][Ni(6.00)]O(20)(OH)(4)[Na(0.86)]·14H(2)O (SAP-2) saponite clays in the temperature range 200-310 K as studied by quasielastic neutron scattering technique. Particularly the effect of the ion substitution towards the dynamics of water is addressed here. Data analysis is carried out using the relaxing cage model. The existence of distribution in relaxation times indicated that the water molecules in saponite clay have a different local environment which leads to complex diffusion behavior. It is found that water exists in a supercooled state in the temperature range up to 235 K. However, some of the water molecules are found to be immobile in the temperature range 240-285 K. The fraction of immobile water decreases with increase in temperature. At higher temperatures, some of the water molecules in the hydration shells or those near the surface start participating in the diffusion process and at 293 K, almost all water molecules contribute to the dynamics. Diffusivity of water in both SAP-1 and SAP-2 are found to be lower in comparison to the bulk, and within the two samples of saponite clay diffusivity in SAP-1 is found to be lower compared to SAP-2; this has been explained on the basis of the charge on the tetrahedral layers and the charge balancing cations in the interlayer spacing.