  In this article, we tentatively assign the $Z_c(4600)$ to be the
$[dc]_P[\bar{u}\bar{c}]_A-[dc]_A[\bar{u}\bar{c}]_P$ type vector tetraquark
state and study its two-body strong decays with the QCD sum rules based on
solid quark-hadron duality, the predictions for the partial decay widths
$\Gamma(Z_c^-\to J/\psi \pi^-)=41.4^{+20.5}_{-14.9}\,\rm{MeV}$,
$\Gamma(Z_c^-\to \eta_c\rho^-)=41.6^{+32.7}_{-22.2}\,\rm{MeV}$,
$\Gamma(Z_c^-\to J/\psi a_0^-(980))=10.2^{+11.3}_{-6.7}\,\rm{MeV}$,
$\Gamma(Z_c^-\to \chi_{c0}\rho^-)=3.5^{+6.7}_{-3.0}\,\rm{MeV}$,
$\Gamma(Z_c^-\to D^{*0} D^{*-})=39.5^{+29.6}_{-19.3}\,\rm{MeV}$,
$\Gamma(Z_c^-\to D^{0} D^{-})=6.6^{+4.6}_{-3.0}\,\rm{MeV}$ and $\Gamma(Z_c^-\to
D^{*0} D^{-})=1.0^{+1.0}_{-0.6}\,\rm{MeV}$ can be confronted to the
experimental data in the future to diagnose the nature of the $Z_c(4600)$.
