Dual Spin Excitation Components in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>FeSe</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0.67</mml:mn> </mml:mrow> </mml:msub> </mml

Iron chalcogenide superconductors FeSe_{1-x}Ch_{x} (Ch=S,Te) exhibit an unusual double-dome superconducting phase diagram, the microscopic origin of which remains unclear. Here, we use inelastic neutron scattering to probe spin excitations in single-crystalline FeSe_{0.67}Te_{0.33}, positioned at the superconducting transition temperature (T_{c}) minimum between the two domes. We identify two distinct spin excitation components separated by a crossover energy (E_{c}≈30 meV). Below E_{c} the spin excitations emanate from the stripe-type wave vector (1,0), with their intensity strongly suppressed upon warming above the nematic transition at T_{s}≈40 K, revealing strong coupling between them. Above E_{c} the high-energy excitations disperse more steeply and display little temperature dependence across T_{s}. Further warming from T_{s} to 300 K results in the gradual downward evolution of the high-energy spin excitations, reaching an incommensurate wave vector near (1,±0.3) at the low-energy limit. The combined energy- and temperature-dependent responses point to competition between stripe and incommensurate excitations, which can contribute to the reduced T_{c} near the valley composition; while Te substitution may simultaneously tune the electronic structure in ways that could coexist with, or reinforce, this competition. These findings illuminate the intricate interplay of multiple components of magnetic excitations in shaping T_{c} of iron chalcogenides.