Laser metal deposition (LMD) is an additive manufacturing process with an extreme potential in large-scale metal production. Among the printable metals, the Inconel 625 has found a wide variety of cutting-edge applications in the aerospace, defense, and space sectors. Thus, knowledge of mechanical properties under quasi-static and dynamic conditions is fundamental. In this work, the quasi-static and dynamic compression behavior of Inconel 625 obtained by LMD is presented. The curves of printed Inconel 625 showed a change in slope in the work hardening phase, which is due to the mechanics of the dislocation motion. Therefore, a modified two-stage (TS) Hollomon power-law is proposed to model this specific mechanical behavior, which identifies a threshold strain that delimit two different hardening behaviors. Furthermore, Johnson–Cook and Cowper–Symonds models were used to represent the effect of strain rate and temperature on the material properties. A variable strain rate sensitivity along the compression strain was found. Hence, double sensitivity terms were introduced into the TS Hollomon power-law, allowing to reproduce the dynamic behavior of Inconel 625.