The use of nontraditional soil stabilizers increases. Various new soil binding agents are under study to augment renewability and sustainability of an earth structure. However, despite increasing interest involved in red clay, there is minimal research investigating the stabilizing red clay with polymer. This paper presents the findings obtained by applying the acrylic polymer and epoxy emulsion as binding agent for red clay and that for sand. The epoxy–hardener ratio, amount of epoxy emulsion, and amount of polymer aqueous solution were manipulated to quantify their effects on red clay and sand, respectively. After compacting a pair of cylindrical samples of which diameter and height are 5 cm and 10 cm, respectively, it is cured for 3 and 7 days in a controlled condition. Each pair is produced to represent the engineering performance at each data point in the solution space. An optimal composition of the binding agents for red clay and that for sand mixture are identified by experimenting every data point. In addition, given lime into each sample, the maximum unconfined compressive strength (UCS) endured by red clay sample and that by sand sample are 2243 and 1493 kPa, respectively. The UCS obtained by the sample mixed with clay and sand reaches 2671 kPa after seven days of curing. It confirms that the addition of lime remarkably improves the UCS. When the clay–sand mixture, of which the ratio is 70:30, includes 5% lime, the UCS of the mixture outperforms. Indeed, these findings, i.e., the optimal proportion of components, may contribute to the increase of initial and long-term strength of an earth structure, hence improving the renewability and sustainability of the earth construction method.