When a body moves on a circular path in outward direction it will move on the tangent to that circle ie direction of the motion along the tangent to the circle any point in its motion.
OR
when the man holds the disc,it have a centeicpetal force and therefor the disc also moves with the man in circular path
when the man releases it,the body will move tangent to the circular path at that point.
because a body in a circular motion have the direction of its velocity as tangent to the circle at any point
hope you understand this
please like if you are satisfied