Silver nanoparticles (Ag-NPs) are attracting great attention for their use in various applications, along with methods for their green and facile production. In this study, we present a new eco-friendly approach based on the use of Euphorbia balsamifera extract (EBE) in the green synthesis of silver nanoparticles (Ag-NPs), which are then applied as a reducing and stabilizing agent for the efficient removal of water-based reactive dyes such as bromocresol green (BCG) and bromophenol blue (BPB). The as-prepared Ag-NPs are quasi-spherical in shape, with an average diameter of 20–34 nm. Diverse characterization methods, including X-ray diffractometry (XRD), Fourier transform infrared spectroscopy (FT-IR), scanning electron microscopy (SEM), transmission electron microscopy (TEM), and Brunauer–Emmett–Teller (BET) analysis, were used to analyze these Ag-NPs. The results reveal that water-soluble biomolecules in the Euphorbia balsamifera extract play an important role in the formation of the Ag-NPs. The removal of toxic dyes was studied under varied operational parameters such as Ag-NP dosage, initial dye concentration, pH, stirring time, and temperature. Under the optimum investigated conditions, nearly 99.12% and 97.25% of the bromocresol green and bromophenol blue dyes, respectively, were removed. Both BCG and BPB adsorption were found to adhere to pseudo-second-order kinetics (r22 = 1 and 0.995) and fit the Langmuir isotherm models well (R12 = 0.998 and 0.994), with maximal monolayer adsorption capacities of 20.40 and 41.03 mg/g, respectively. Their adsorption processes were observed to be intrinsically endothermic. The results confirm the potential of the Euphorbia balsamifera extract as a low-cost, nontoxic, and eco-friendly natural resource for the synthesis of Ag-NPs that may be useful in the remediation of hazardous dye-contaminated water sources.