Let our frame of reference be the center of this circle. After the string is released, in this frame, there is no net force on the rock (we are pretending our system is isolated, i.e., we are ignoring things like gravity that we would obviously have to take into account in the 'real world'). Under the assumption that our frame of reference is inertial, this implies that the acceleration of the rock is $0$, i.e., has constant velocity. To figure out what this constant velocity is, just look at whatever the velocity was just before the string was released. It was moving tangent to the circle before (this motion was forced on it by the tension in the string), and hence it will 'fly out' on a line tangent to the original circle.