This study is devoted to recovering two initial values for a time-fractional diffusion-wave equation from boundary Cauchy data. We provide the uniqueness result for recovering two initial values simultaneously by the method of Laplace transformation and analytic continuation. And then we use a nonstationary iterative Tikhonov regularization method to solve the inverse problem and propose a finite dimensional approximation algorithm to find good approximations to the initial values. Numerical examples in oneand two-dimensional cases are provided to show the effectiveness of the proposed method.