In this work, we use computational design to examine 15 new electrolyte salt anions by performing chemical variations and mutations on the bis(trifluoromethane)sulfonamide (TFSI) anion. On the basis of our calculations, we propose two new anions as potential candidates for magnesium energy-storage systems, which are evolved from TFSI with the substitution of sulfur atoms in TFSI and the modification of functional groups. The applicability of these new anion salts is examined through comprehensive calculations using both first-principles as well as benchmarked classical molecular dynamics. We elucidate the important properties of these anions, including the electrochemical stability window, chemical decomposition, preferred solvation structure, diffusion coefficient, and other dynamical properties for 15 rationally designed molecules. Two of the designed anions are found to successfully avoid the vulnerability of TFSI during ion-pair charge-transfer reactions while retaining comparable or better performance of other properties. As such, our work provides, to our knowledge, the first theoretically designed electrolyte salt for contemporary multivalent batteries and provides guidance for the synthesis and testing of novel liquid electrochemical systems.