This article discusses a new technology of forming connector forgings from ZK60 magnesium alloy preforms by die forging on a screw press. The purpose of the study was to evaluate the feasibility of using preforms cast from the ZK60 magnesium alloy to forge a connector forging with improved mechanical properties compared to those obtained by casting. It also aimed to establish whether this new forging method has the potential for replacing the multi-stage forging process conducted on hydraulic presses used for high-strength Mg alloys. A numerical analysis of the proposed approach was performed by the finite element method, applying the popular DEFORM computer software for simulating forming processes. The numerical results confirmed that the developed method produces parts with the desired shape. The numerical results also provided information regarding the behavior of the workpiece’s material and the screw press forging process, including the distributions of strains and temperatures, the Cockcroft–Latham damage criterion, and energy required to form connector forgings. The proposed screw press forging process for producing ZK60 alloy connectors from cast preforms was verified by experimental tests. The connector forgings produced from the ZK60 magnesium alloy were then subjected to qualitative tests.