Based on the extended Huygens-Fresnel principle, the propagations of a partially coherent vortex beam through atmospheric turbulence along an uplink path and a downlink path are studied, where the Gaussian Schell-model (GSM) vortex beam is taken as a typical example of partially coherent vortex beam. The analytical expressions for the average intensity, rms width and cross-spectral density function of GSM vortex beam propagating through atmospheric turbulence along a slant path are derived and used to study the influence of atmospheric turbulence along an uplink path and a downlink path on GSM vortex beam propagation and on coherence vortex. It is shown that under the same conditions the influence of atmospheric turbulence along a downlink path on GSM vortex beam propagation is smaller than that along a uplink path, and the conservation distance of the topological charge of GSM vortex beam along a downlink path is longer than that along a uplink path. The results are explained in physics.