Let (S,\rho) be an ultrametric space with certain conditions and S^k be the quotient space of S with respect to the partition by balls with a fixed radius \phi(k) . We prove that, for a Hunt process X on S associated with a Dirichlet form (\mathcal E, \mathcal F) , a Hunt process X^k on S^k associated with the averaged Dirichlet form (\mathcal E^k, \mathcal F^k) is Mosco convergent to X , and under certain additional conditions, X^k converges weakly to X . Moreover, we give a sufficient condition for the Markov property of X to be preserved under the canonical projection \pi^k to S^k . In this case, we see that the projected process \pi^k\circ X is identical in law to X^k and converges almost surely to X .