We study scalar-tensor-tensor cross correlation $langle zeta hh rangle$ generated by the dynamics of interacting axion and SU(2) gauge fields during inflation. We quantize the quadratic action and solve the linear equations by taking into account mixing terms in a non-perturbative manner. Combining that with the in-in formalism, we compute contributions from cubic interactions to the bispectrum $B_{zeta hh}$. We find that the bispectrum is peaked at the folded configuration, which is a unique feature encoded by the scalar mixing and localized production of tensor modes. With our parameter choice, the amplitude of the bispectrum is $k^6 B_{zeta hh} sim 10^{-16}$. The unique shape dependence, together with the parity-violating nature, is thus a distinguishing feature to search for in the CMB observables.
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