Nuclear matrix elements (NMEs) for double beta decays (DBDs) are crucial for studying the neutrino mass and other neutrino properties beyond the standard electro-weak model by measuring neutrino-less DBDs. The spin-dipole (SD) J ^π = 2^- NME is one of the major components associated with the DBD NME. The SD NME for ⁷⁶Ge was derived for the first time by using the ^74,76 Ge (³He, t) at RCNP Osaka. The obtained SD NME for the ⁷⁶Ge → ⁷⁶As ground-state transition is in natural units. This is smaller by a coefficient around k ≈ 0.2 with respect to the quasi-particle model NME. The impact of the reduced (quenched) SD NME on DBD neutrino studies is discussed.