The Caesalpinia spinosa plant, known as Tara, was used to prepare a green corrosion inhibitor solution using hot solid-liquid (Soxhlet extraction, Tara-SE) and cold solid-liquid extraction (maceration, Tara-ME) techniques. Their anticorrosive protection ability was tested on mild steel in a 0.1 M HNO3 solution. The chemical content of the extracts was examined by FTIR and Vis spectrophotometry, and the surface morphology of the mild steel was studied by SEM. The effect of different concentrations of the green inhibitors on the mild steel in acidic solutions was determined by weight loss (WL), potentiodynamic polarization (PP), and electrochemical impedance spectroscopy (EIS) measurements, allowing the estimation of the inhibitor efficiency (IE%). Values of IE ranging from 90.73 to 97.38% for Tara-1000-SE and from 85.3 to 96.05% for Tara-1000-ME were obtained by WL, PP, and EIS experiments. The thermodynamic assessments at different temperatures and concentrations were studied using different adsorption isotherm models (i.e., Langmuir, Freundlich, Temkin, Flory-Huggins, and El-Awady). The best results were confirmed by the best values of the simultaneous R and reduced-Chi-squared statistical parameters. The Gibbs free energy of adsorption (ΔGads) value suggests that the inhibitor is physically absorbed on the metal surface. The adsorption mechanism, studied by classical and computational quantum mechanical modeling methods, evidenced strongly developed interactions between gallic acid adsorbate (i.e., the principal component of the Tara extract) and differently cleaved Fe surfaces. Moreover, density functional theory (DFT) based electron localization function (ELF) analysis assessed the nature of these interactions as being characteristic of physisorption processes. The results showed superior inhibition performance of the hot solid-liquid extraction (Soxhlet extract, SE) compared to the cold solid-liquid extraction techniques (maceration, ME), although, according to all research techniques, both extracts demonstrated a satisfactory level of anticorrosive protection for the mild steel exposed to acid conditions.