I am not sure if I understand how forces work during hammerthrow. From my understanding athlete works with Fmuscle force on a ball and rotate it and a ball works with equal opposite force on an athlete causing rotation in a opposite direction. The mass of athlete is greater than the mass of ball so athlete rotates with ball in 1 direction(Fmuscle direction). Does it mean if ball would be heavier(more massive) than athlete, the athlete could not rotate it(even if strong enough to move it) ?

You have you diagram wrong.

 

 

There are no tangential forces acting. (well almost).

 

The muscle power (and weight behind it) act radially towards the centre, as the athlete leans backwards.

 

The athlete builds up the rotation of the hammerweight by slight angling his inward pull off centre so that a small circumferential acceleration allows him to swing the ball round.

 

As soon as he lets go the hammerball obeys Newton's First Law and flies off at a tangent in a straight line since there are no longer any forces acting on it.

 

The inward acting force is called the centripetal force.