Vortex $\ensuremath{\gamma}$-ray beams with large orbital angular momentum (OAM) have significant potential applications in material science, nuclear detection, and astrophysics. An all-optical scheme for production of intense vortex $\ensuremath{\gamma}$-ray beams using relativistic laser-plasma interactions is proposed, where the OAM of $\ensuremath{\gamma}$-photons is converted from the spin angular momentum of circularly polarized (CP) lasers. The spin-to-orbital angular momentum conversion is achieved by two processes: resonant acceleration of electrons in CP laser-plasma interactions and nonlinear Compton scattering (NCS) of another linearly polarized laser from the former. Three-dimensional particle-in-cell simulations show that vortex $\ensuremath{\gamma}$-ray beams with a large and controllable OAM of $2.5\ifmmode\times\else\texttimes\fi{}{10}^{18}\ensuremath{\hbar}$ and energy up to hundreds of $\mathrm{MeV}$ can be obtained by using two lasers at intensities of approximately ${10}^{22}\phantom{\rule{0.2em}{0ex}}{\mathrm{W}/\mathrm{cm}}^{2}$, which is much more practical and more efficient than previously proposed NCS of a Laguerre-Gaussian beam.