We use transport and neutron scattering to study the electronic phase diagram and spin excitations of NaFe1−xCuxAs single crystals. Similar to Co- and Ni-doped NaFeAs, a bulk superconducting phase appears near x≈2% with the suppression of stripe-type magnetic order in NaFeAs. Upon further increasing Cu concentration the system becomes insulating, culminating in an antiferromagnetically ordered insulating phase near x≈50%. Using transport measurements, we demonstrate that the resistivity in NaFe1−xCuxAs exhibits non-Fermi-liquid behavior near x≈1.8%. Our inelastic neutron scattering experiments reveal a single neutron spin resonance mode exhibiting weak dispersion along c axis in NaFe0.98Cu0.02As. The resonance is high in energy relative to the superconducting transition temperature Tc but weak in intensity, likely resulting from impurity effects. These results are similar to other iron pnictides superconductors despite that the superconducting phase in NaFe1−xCuxAs is continuously connected to an antiferromagnetically ordered insulating phase near x≈50% with significant electronic correlations. Therefore, electron correlations is an important ingredient of superconductivity in NaFe1−xCuxAs and other iron pnictides.