Newton's First Law of motion states that an object will continue to move in a straight line or remain at rest unless a force acts on it
The stone is able to move in circular motion because a (centripetal) force acts through the string on it, which maintains the circular motion, by turning the stone to the circular path as the stone moves with momentary velocity along a straight line which is (therefore) tangential to the circle
Therefore, at the point the spring breaks, the centripetal force is no longer acting on the stone to change its path and the motion of the continues on the tangent to the initial circular motion path at that point
