The balanced amelioration of mechanical characteristics of fat clay with an additive refers to the attainment of high strength without compromising ductility, which is unattainable by solitary usage of a cementing additive. For this purpose, an amalgamated binary admixture (ABA) is proposed by assimilating shredded face mask (FM) waste, which is posing serious environmental concerns these days, with a cementitious waste material, i.e., silica fume (SF). However, for such ABA, the optimization of mix design is desirable because an excessive amount of one component could disturb the required balance. To address this issue, response surface methodology (RSM) is used in the current study, which is a strong technique used during the process of production to develop, improve, and optimize product inputs. Several experiments are designed and conducted to evaluate mechanical responses, i.e., unconfined compressive strength (
q
u
), brittleness index (
I
B
), deformability index (
I
D
), and California bearing ratio (
CBR
) value, of treated fat clay by varying mix designs of ABA. Based on the test results, mathematical models are developed which are found to be statistically valid to predict the subjected responses using SF and FM as inputs. Afterward, an optimized mix design is determined by integrating developed models with a desirability function model and setting maximization of strength and ductility as the optimization goals. An ABA having 7.9% SF and 1.2% FM is observed to provide the highest strength and ductility for multiple applications, i.e., road and buildings, with desirability factor close to unity; responses of which are also validated by performing tests. Furthermore, analysis of cleaning aspect shows that the use of optimized ABA in place of cement for subgrade improvement of 1 km two-lane road could avoid CO
2
emission of around 79,032 kg of C, save 42,720 kWh and 1174.8 GJ of electrical and thermal energy, respectively, and clean 43 Mg of FM waste; however, astute protocols of COVID-19 FM waste handling and disinfection are needed to be established and followed.