Magnetic topological semimetals have attracted intense attention recently since these materials carry a great promise for potential applications in novel spintronic devices. Here, we report an intimate interplay between lattice, Eu magnetic order and topological semimetallic behavior in Eu$_{1-x}$Sr$_{x}$MnSb$_{2}$ driven by nonmagnetic Sr doping on magnetic Eu site. Different types of Eu spin reorientations are controllable by the Sr concentration, temperature or magnetic field, and coupled to the quantum transport properties of Dirac fermions generated by the 2D Sb layers. Our study opens a new pathway to achieving exotic magnetic order and topological semimetallic state via controlling spin reorientation. The effective strategy of substituting rare-earth site by nonmagnetic element demonstrated here may be applicable to the AMnCh$_{2}$ (A=rare-earth elements; Ch=Bi/Sb) family and a wide variation of other layered compounds involving spatially separated rare-earth and transition metal layers.