Estimation of the jump activity index from high frequency observations has received a lot of attention in recent years since the jump activity index can be used for different purposes, especially in financial field. The work focuses on the estimation of the Blumenthal-Getoor index of a stochastic differential equation driven by a truncated stable process with index in (0,2) based on high frequency observations on a fixed time period. We construct estimators of the index based on the two moment-fitting procedures (the logarithmic moments and the lower-order fractional moments). We derive consistency and asymptotic normality for the estimators of the index parameter. Finally we give some simulations to illustrate the finite-sample behaviors of our estimators.