We report an inelastic neutron scattering investigation on the spin resonance mode in the optimally hole-doped iron-based superconductor Ba_0.67K_0.33Fe₂As₂ with T_c = 38.2 K. Although the resonance is nearly two-dimensional with peak energy E_R ≈ 14 meV, it splits into two incommensurate peaks along the longitudinal direction ([H,0,0]) and shows an upward dispersion persisting to 26 meV. Such dispersion breaks through the limit of total superconducting gaps Δ_tot = |Δ_k|+|Δ_k+Q| (about 11-17 meV) on nested Fermi surfaces measured by high resolution angle resolved photoemission spectroscopy (ARPES). These results cannot be fully understood by the magnetic exciton scenario under s^±-pairing symmetry of superconductivity, and suggest that the spin resonance may not be restricted by the superconducting gaps in the multi-band systems.