Let Omega subset of R-N be a bounded domain with a Lipschitz continuous boundary. We study the controllability of the space-time fractional diffusive equation {D(t)(alpha)u+(-Delta)(s) u = 0 in (0, T) x Omega, u = g chi((0, T)) (x) (O) in (0, T) x (R-N \ Omega), u(0, .) = u(0) in Omega}, where u = u(t, x) is the state to be controlled and g = g(t, x) is the control function which is localized in a nonempty open subset O of R-N \ Omega. Here, 0 < alpha <= 1, 0 < s < 1, and T > 0 are real numbers. After giving an explicit representation of solutions, we show that the system is always approximately controllable for every T > 0, u(0) is an element of L-2(Omega), and g is an element of D((0, T) x O), where O subset of R-N \ Omega is an arbitrary nonempty open set. The results obtained are sharp in the sense that such a system is never null controllable if 0 < alpha < 1. The proof of our result is based on a new unique continuation principle for the eigenvalues problem associated with the fractional Laplace operator subject to the zero Dirichlet exterior condition that we have established.