We show that the wave function in one spatial sector x1<x2<⋯<xN (with xi being the coordinate of the ith particle) of a one-dimensional spinor gas with contact s-wave interaction, either bosonic or fermionic, can be mapped to the direct product of the wave function of a spinless Fermi gas with short-range p-wave interaction and that of a spin system governed by spin-parity projection operators. Applying this mapping to strongly interacting spinor gases, we obtain a generalized spin-chain model that captures both the static and dynamics properties of the system. Using this spin-chain model, we investigate the breathing-mode frequency and the quench dynamics of strongly interacting, harmonically trapped spinor gase