Quantum droplets (QDs) are a recently discovered new state of matter in ultracold atoms. We study threedimensional (3D) self-trapped modes in spinor Bose-Einstein condensates with spin-orbit coupling (SOC), described by coupled Gross-Pitaevskii equations including beyond-mean-field Lee-Huang-Yang terms. The 3D QDs, semi-vortex and mixed-mode states, of a large size with an anisotropic density profile, exist with a wide large values of the norm as the Lee-Huang-Yang terms eliminate the collapse. The effect of the intra- and intercomponent of the nonlinearity and SOC on characteristics of the QDs is systematically addressed. Using the linear-stability analysis and direct simulations, we have checked the stability of all the 3D QDs states, stressing they are stable against small perturbations in propagation in limited scales. The present analysis opens a new way for creating multidimensional solitary waves, and may be developed in other directions, including nonlinear optics, not only in conservative, but also in dissipative systems.