C

Step 1: Understand the forces acting on the stone.
When the stone is rotated in a circle, it requires a centripetal force to keep it moving in that circular path. This centripetal force is directed towards the center of the circle.
Step 2: Analyze what happens when the string is cut.
Once the string is cut, the centripetal force is removed. According to Newton's first law of motion, an object in motion will remain in motion at constant velocity in a straight line unless acted upon by an external force.
Step 3: Explain the concept of inertia.
The stone has inertia, which is the tendency of an object to resist changes to its state of motion. In this case, the stone will continue moving in the direction it was heading at the instant the string was cut, which is tangential to the circle.
Conclusion: Hence, the stone flies away in a direction tangent to the circle due to its inertia; therefore, the correct answer is C.