Nontrivial topological band structures in semiconductors such as chiral materials give rise to intriguing topological phases, unique spin texture, and novel quantum physical phenomena. However, the transport behaviors of two-dimensional Weyl semiconductors with the Fermi level adjacent to Weyl nodes are seldom explored. Here, we systematically investigate the magnetoresistance (MR) and nonreciprocal transport of the two-dimensional tellurene nanostructure with unexpected phenomena. With the participation of the Weyl nodes in the carrier transport, an unreported negative MR is obtained in the weak magnetic field range of 0−2 T. Additionally, because of the Fermi surface splitting induced by the Weyl nodes, the onset magnetic field required for quantum oscillation was reduced to ∼3.5 T which is much lower than that in bulk tellurium (10 T). Moreover, a perpendicular spin component is observed in the Fermi surface near the Weyl nodes, which is detected by the angle-dependent measurement of the nonreciprocal signal of bilinear magnetoresistance. This work deepens the understanding of Weyl physics and highlights an efficient way for the detection of nonreciprocal transport and the construction of corresponding spin texture. The results pave the way for potential applications in designing topological semiconductor devices.