This study includes the characterization and exploitation of an abundant agricultural waste in Algeria, Alfa (Stipa tenacissima L.) leaf powder (ALP) as a biosorbent for the removal of hazardous triphenylmethane dyes, malachite green (basic green 4) and crystal violet (basic violet 3), from aqueous media under various operating conditions in batch mode. The effect of experimental parameters such as initial dye concentration (10–40 mg/L), contact time (0–300 min), biosorbent dose (2.5–5.5 g/L), initial pH (2–8), temperature (298–328 K), and ionic strength on dye sorption was investigated. The results of both dyes show that the increase in initial concentration, contact time, temperature, and initial pH of solution leads to an increase in biosorbed quantity, unlike the effect of ionic strength. The biosorption kinetics for triphenylmethane dyes on ALP was analyzed by pseudo-first-order, pseudo-second-order, Elovich, and intraparticle diffusion models proposed by the Weber–Morris equation. Equilibrium sorption data were analyzed by six isotherms, namely the Langmuir, Freundlich, Harkins–Jura, Flory–Huggins, Elovich, and Kiselev isotherms. The thermodynamic parameters were evaluated for both dyes. The thermodynamic results suggest that both dyes’ biosorption is a typical physical process, spontaneous and endothermic in nature.