  In this work we extend the $q_T$-subtraction formalism, originally developed
for QCD corrections, to the case of mixed QCD$\otimes$QED corrections, and
apply it to the fully exclusive calculation of the ${\cal{O}}(\alpha_s\alpha)$
contribution to the production of an off-shell $Z$ boson in hadronic
collisions. We present explicit results for the subtraction term and the hard
factor, therefore providing all the ingredients needed for the application of
the formalism up to ${\cal{O}}(\alpha_s\alpha)$. To study the phenomenological
impact we consider the decay of the off-shell $Z$ boson into a pair of
neutrinos, and present kinematical distributions for the final-state leptons at
LHC energies.
