Mechanically driven complex concentrated alloys can be formed by three or more types of elemental powders mixing into a solid solution through severe plastic deformation at temperatures much lower than the melting point of each element. While competition between the thermal and mechanical driving forces during forced mixing of binary systems with positive enthalpy of mixing is relatively well understood, the physics of mechanically driven mixing of multiple elements with negative mixing enthalpies remained unclear. In this work, we combined mechanical alloying (MA), X-ray diffraction (XRD), and kinetic Monte Carlo (kMC) simulations to systematically study the interplay between the chemical pairing potential and the mechanical strength of elemental pairs during the formation process of mechanically driven complex concentrated alloys. We demonstrate that the chemical and mechanical forces play a competing role in the mixing of ternary complex concentrated alloys with negative mixing enthalpies. The chemical driving force favors a chemically ordered atomic structure, while the mechanical force encourages a random atomic arrangement. We reveal the energetic basis of this competition as the gain and loss in mixing enthalpy and configurational entropy. Following this fundamental understanding, three types of mixing mechanisms and their corresponding steady-state phases are defined. We show that the molar content of the element with the lowest average mixing enthalpy governs the mixing mechanisms and thus determines the energetic stabilization of the steady-state phases. A theoretical phase prediction map is provided for alloy design. We synthesized a nanocrystalline equiatomic NiCoCr coating under the guidelines of the map, which presents exceptional mechanical properties achieved by the mechano-chemical mixing.