Why dont you show us the math..?
He won't be able to do that maths.
1) He wouldn't know where to start. His limit of maths is knowing that when he goes to the bar to order two pints of lager and a packet of crisps he has to pay for three items.
2) The string being in tension is what is keeping the ball from flying off. When the string is cut, the string right next to the ball remains in tension until the 'wave' from the cut end reaches that point. The wave takes time to move down the string and is not instantaneous. So the maths would prove him wrong.
I'm guessing the maths would require some integral calculus and I'm also guessing the ball would not fly off at a tangent, more of a parabola until all external forces on the ball resolved to zero.