  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.
