We study a nonuniform strain in zigzag graphene nanoribbons for producing the spin-thermoelectric effects, using the mean-field Hubbard approximation and a Green's function approach. Our theoretical results show that a sinusoidal-shaped inhomogeneous strain with electron-electron interaction could induce a different effect on each edge of zigzag nanoribbons and finally generate a spin semiconductor with a tunable spin-dependent band gap. The strength of strain also controls the magnitude of magnetization in each edge. Interestingly, pure spin current and a giant spin Seebeck coefficient can be produced even at low values of strain by applying a thermal gradient and without magnetic elements. These results pave a practical way toward improved design for spin-thermoelectric applications through strain engineering.