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Based on the extended Huygens-Fresnel principle, the analytical expressions for the cross-spectral density function of mixed circular edge-screw dislocations beams propagating through atmospheric turbulence have been derived, and used to study the dynamic evolution of mixed circular edge-screw dislocations in free space and atmospheric turbulence. It is shown that the radius of circular edge dislocations increases with increasing propagation distance, and both the positions of the optical vortex and the center of circular edge dislocations are located at the point (0, 0) when mixed circular edge-screw dislocations propagate in free space. When mixed circular edge-screw dislocations propagate in the atmospheric turbulence, the position of optical vortices varies with increasing propagation distance, the circular edge dislocation evolves into a pair of optical vortices with the opposite topological charge ±1, and the pair of optical vortices will annihilate as soon as the propagation distance becomes large enough. [ABSTRACT FROM AUTHOR]