The co-occurrence of phase transitions with local and global order parameters, such as entangled magnetization and topological invariants, is attractive but seldom realized experimentally. In this study, a magneto-topological phase transition (magneto-TPT), that is, the phenomenon of magnetic materials undergoing different magnetic and topological phases during pressure loading, is investigated. By considering both out-of-plane ferromagnetic and in-plane antiferromagnetic components, it is discovered that the calculated results fit well with the experimental data. The calculation results further reveal a pristine Weyl phase with four additional pairs of Weyl nodes under low pressure, and a generally defined Z 2 topological insulator phase after the restoration of time-reversal symmetry at 40.4 GPa. The transport measurements performed at 5 K reveal that the magnetic order almost vanishes at 40.3 GPa, which is consistent with the theoretical prediction. Moreover, the present magneto-TPT involves the degeneration of a pair of crossing bands of two spin channels. Hence, all the chiral Weyl nodes annihilate with their counterparts from another spin channel, in contrast to the typical intraband annihilation of Weyl pairs in inversion-asymmetric systems. The study reveals a method for realizing diverse topological states by modulating exchange splitting by external physical knobs such as pressure in topological magnets.