A, the athlete's speed is increasing in the run-up stage, so the kinetic energy becomes larger and the gravitational potential energy remains unchanged; Therefore, mechanical properties will increase; So, A is wrong;

B, when taking off, the athlete has both speed and height, so the athlete has both kinetic energy and gravitational potential energy; Therefore, its mechanical energy is not zero; So, B is wrong;

C, after the highest point, the athlete's height is the largest, so the gravitational potential energy is the largest; Therefore, C is correct;

D, during the descent, the gravitational potential energy decreases and the kinetic energy increases; So gravity potential energy is converted into kinetic energy; So, d is wrong.

So choose C.