We investigate the ground-state phases and spin-scissors dynamics of binary Bose-Einstein condensates confined in a twisted two-dimensional harmonic trap. The ground state hosts three distinct phases (phase-separated, polarized, and phase-mixed) determined by the Rabi coupling, interaction ratio $G$ (between intercomponent and intracomponent interactions), and spin-twisting, which induces edge-localized polarization through position-dependent detuning. In the phase-mixed regime, the ground state is characterized by a finite spin-scissors susceptibility and can be accurately described using local density approximation. In the dynamics, the system exhibits stable periodic beating in the phase-mixed state for $G\le 1$. For $G>1$, its evolution progresses from beat damping (phase-separated state) to polarized relaxation (polarized state), finally reaching stable periodic beating (phase-mixed state) after a finite waiting time. The dependence of the waiting time contrasts sharply with the monotonic behavior of one-dimensional spin-dipole dynamics, revealing qualitatively distinct mechanisms governed by geometry and interactions. In summary, these results establish a unified link between ground-state properties and nonequilibrium responses in twisted spinor condensates, offering a versatile platform for exploring spin-related quantum many-body phenomena.

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• Bose-Einstein condensates
• Collective effects in atomic physics