The paper is devoted to the study of the mechanical, microstructural, and bio-corrosive behavior of low-alloyed Zn–Mg biodegradable surgical wires for bone reconstructions. Three biodegradable alloys with different magnesium content have been studied, their production technology has been developed and the product properties have been determined. The technology includes casting, extrusion, hot and cold drawing of the wire, and the product surface finishing. The paper shows the most important stages of the process (i.e., extrusion and drawing) in detail. The technological parameters have been selected based on the results of the computer modeling. The flow stress–strain curves of extruded materials have been obtained at various strain rates and temperatures. Two drawing technologies have been compared. The first one is the room temperature conventional wire drawing. In the second one, the first few passes have been made at an elevated temperature and the rest at room temperature. This allowed avoiding the breaking of the wire during the first passes (a typical issue of the conventional technology for these alloys) and increasing the ductility of the final product. Mechanical properties, bio-corrosion, and crystallographic texture of the material were determined at different stages of the processing. A simultaneous increase in the wire strength, the number of repeated bending until the rupture of the wire, and in the bio-corrosion rate due to drawing has been registered. This phenomenon coincided with a change in the crystallographic texture. It has been shown that the product tensile strength of about 250–300 MPa can be reduced by about 30% due to surgical knots tied on it.