We report the formation of H2+ and C2+ from dissociation of acetylene induced by α-particle irradiation. The unusual dissociation channel [C2H2]2+ → H2+ + C2+ is unambiguously identified by measuring the time-of-flight of both fragmented ions in coincidence. Our quantum chemical calculation confirms the existence of this dissociation pathway. It shows that [HCCH]2+ is firstly populated to the 3Π excited electronic state, followed by acetylene-vinylidene isomerization, and finally the vinylidene-like intermediate dissociates to H2+ and C2+. This dissociation channel is the simplest prototypical reaction involving H migration, H-H combination, and C-H bond cleavage. The current study plays an important role for understanding the H2+/H3+ formation reactions from organic di-cations in an interstellar medium.