The need for retrofitting existing masonry structures is progressively becoming more important due to their continuous deterioration or need to meet the current design requirements of Eurocodes. Textile-Reinforced Mortar (TRM) composite systems have emerged as a sustainable repair methodology suitable for structure retrofitting. Nevertheless, their mechanical performance is still far from being fully investigated. This paper presents an experimental study on the tensile and bond behaviors of a new mortar-based composite consisting of mineral additives, blended cement mortar, and stainless-steel grid. Three different mineral additives (silica fume, fly ash, and blast furnace slag), in binary and ternary systems were used. The experimental study included uniaxial tensile coupon testing on composite specimens and bond tests on composite material applied to clay-brick substrate. The results obtained with the different textile-reinforced cement-based mortars were compared and are discussed here. It was found that, for mortar formulations containing mineral additives—such as fly ash or blast-furnace slag—with high tensile and bond strengths, an adequate adherence between the constituents was obtained. The developed mortar presents mechanical performances equivalent to traditional mortars without additives. The study contributes to the existing knowledge regarding the structural behavior of TRM and promotes the development of a low impact carbon cementitious matrix.