In this study, Zn-xCu (-0.1 Mg) wires with a diameter of 0.3 mm were obtained by hot extrusion and cold drawing. The microstructures, mechanical properties, and degradation behaviour were investigated to evaluate their feasibility as biodegradable metals. During the drawing process of the Zn-xCu alloys, many granular CuZn5 phases were dynamically precipitated, and the grains were significantly refined, along with a significant work softening with the tensile strength decreasing and the elongation increasing (from 161 MPa to 92 MPa and 22%–103% for Zn-0.2Cu). With the increase of Cu additions, the phenomenon of work softening was more intense and there was an opposite trend in the strength changes between the as-extruded rods (increase) and as-drawn wires (decrease). With 0.1 wt.% Mg added, the stable rod-like Mg2Zn11 phase was formed in as-extruded Zn-xCu-0.1 Mg rods, which obviously improved the strength, and inhibited the dynamic precipitation of granular CuZn5 phase and work softening phenomenon in the drawing process (from 332 MPa to 313 MPa and 11%–46% for Zn-0.2Cu-0.1 Mg). In addition, due to the micro-galvanic effect induced by the precipitates, alloying accelerated the degradation of Zn alloy wires, especially Zn-1Cu-0.1 Mg, which was related to the shape, distribution, and potential of the phases.