Deformation effects on the spin-isospin responses of nuclei, in particular,
the Gamow-Teller (GT) modes of excitation are investigated in a microscopic framework
based on nuclear density-functional theory.
To describe the low-lying GT states and the GT giant resonance (GTGR) in deformed neutron-rich nuclei,
I employ the Skyrme energy-density functionals in the Hartree-Fock-Bogoliubov calculation
for the ground states and in the Quasiparticle Random-Phase Approximation for the excitations.
It is found that the fragmentation of the strength distribution in the low excitation-energy region
has a strong impact on the $\beta$-decay properties,
while the $K-$splitting is small for the GTGR.