We study an energy relaxation process after many degrees of freedom are highly excited in a Hamiltonian system with a large number of degrees of freedom. Bottlenecks of relaxation, where relaxation of the excited elements drastically slows down, are discovered. By defining an internal state for the excited elements, it is shown that the drastic slowing-down occurs when the internal state is in a critical state. The relaxation dynamics brings the internal state into the critical state, and the critical bottleneck of relaxation is self-organized.