All-oxide-based synthetic antiferromagnets (SAFs) are attracting intense research interest due to their superior tunability and great potentials for antiferromagnetic spintronic devices. In this work, using the La_2/3Ca_1/3MnO₃/CaRu_1/2Ti_1/2O₃ (LCMO/CRTO) superlattice as a model SAF, we investigated the layer-resolved magnetic reversal mechanism by polarized neutron reflectivity. We found that the reversal of LCMO layer moments is mediated by nucleation, expansion, and shrinkage of a magnetic soliton. This unique magnetic reversal process creates a reversed magnetic configuration of the SAF after a simple field cycling. Therefore, it can enable vertical data transfer from the bottom to the top of the superlattice. The physical origin of this intriguing magnetic reversal process could be attributed to the cooperation of the surface spin-flop effect and enhanced uniaxial magnetic anisotropy of the bottom LCMO layer. This work may pave a way to utilize all-oxide-based SAFs for three-dimensional spintronic devices with vertical data transfer and high-density data storage.