We investigate the spin dynamics of SrCr(9p)Ga(12-9p)O19 for p below and above the percolation threshold p(c) using muon spin relaxation. Our major findings are as follows: (i) At T-->0 the relaxation rate is T independent and approximately p(3), (ii) the slowing down of spin fluctuation is activated with an energy U, which is also a linear function of p(3) and lim U as p-->0 = 8 K; this energy scale could stem only from a single ion anisotropy, and (iii) the p dependence of the dynamical properties is identical below and above p(c), indicating that they are controlled by local excitation.