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Pancharatnam-Berry (PB) metasurfaces encode the geometric phase through the rotation of the meta-atom, which exhibits opposite phases and nearly equal conversion amplitudes in the two cross-polarized channels. This spin duality has long restricted PB metasurfaces to spin-symmetric responses with insufficient contrast for spin-selective operation. Here we experimentally demonstrate a regime in which the geometric phase is preserved while its spin duality is deliberately broken. By engineering the pillar-lattice symmetry mismatch together with the etch depth to maximize contrast, we decouple the conversion amplitudes of the two spin channels without affecting the geometric-phase evolution. This enables a spin-asymmetric geometric-phase response that has not been accessible in conventional PB designs. We verify the broken duality through far-field measurements that reveal the selective suppression of the conjugate channel normally enforced by the PB phase. These results establish an accessible pathway to geometric-phase metasurfaces operating beyond their long-standing spin-duality constraint, enabling new forms of spin-dependent wavefront control in optical communications and displays with flat-optical elements.