The utilization of waste rubber as a viable option for manufacturing building materials holds great significance for the sustainable development of the construction industry. This study explores the addition of two additives, fly ash (FA) and glass fiber (GF), to rubberized mortar in order to improve its performance. The impact of different waste rubber powder (RP) replacement rates and modified additive dosages on the performance of rubberized mortar, including fluidity, mechanical properties, drying shrinkage, impact resistance, and thermal insulation properties, was investigated. Furthermore, the analytic hierarchy process (AHP) was adopted to study the priorities of the rubberized mortar modified by FA and GF. The results indicate that the addition of RP leads to a decrease in mortar fluidity, mechanical properties, and drying shrinkage. However, it can enhance its impact resistance and thermal insulation properties. The additives, FA and GF, have a significant influence on the properties of rubberized mortar. By means of AHP method analysis, this study concludes that the optimal comprehensive properties of FA- and GF-modified rubberized mortar can be achieved by replacing 10% of sand with RP and using 10% FA and 0.4% GF. This study presents a configuration method for modified thermal insulation rubberized mortar, and it may lead to FA and GF being considered potential candidates for developing environmentally friendly building materials.