A spin nematic order, analogous to the nematic liquid crystal, characterizes the spontaneous breaking of spin-space rotational symmetry while preserving time-reversal (T) symmetry. In contrast, scalar spin chirality (SSC), a composite three-spin order, breaks T symmetry and is known to induce an anomalous Hall effect (AHE). Although a spin nematic phase has been suggested in frustrated magnets and the square-lattice iridate, how it might affect magnetotransport properties is unknown. Here we use polarized neutron scattering to show that tetragonal AMnBi₂ (A = Ca, Yb) is a strictly c-axis-aligned collinear antiferromagnet (C-type), with T_N ≈ 270 K and 290 K, respectively. On cooling from 450 K to T_N, low-energy spin excitations in YbMnBi₂ spontaneously change from isotropic to anisotropic in spin space within the tetragonal plane, forming a dynamic spin nematic phase around 400 K due to heavy Yb-induced spin-orbit coupling, before gapping out below T_N. Similar measurements on CaMnBi₂ reveal isotropic paramagnetic scattering without a spin nematic phase above T_N. Under an in-plane magnetic field, the Yb³⁺ moments may interact with the dynamic spin nematic phase to induce nonzero SSC, giving rise to AHE and an anomalous Nernst effect (ANE) in YbMnBi₂ that are absent in CaMnBi₂ above T_N. A symmetry-based Ginzburg-Landau analysis shows that coupling terms between the nematic order and SSC are allowed under an external magnetic field, which could explain the rapid increase of AHE with field in YbMnBi₂. Our results provide compelling evidence for dynamic SSC-induced AHE and ANE in the paramagnetic phase of a compensated collinear antiferromagnet, opening a new avenue for the physics of composite spin orders and room-temperature spintronics without magnetic order.