In this study, two by-products resulting from the processing of cherry (stems and pits) were used as natural coagulants to promote the valorization of these wastes and treat olive mill wastewater (OMW). The efficacy of the plant-based coagulants (PBCs) in the coagulation–flocculation–decantation process (CFD) was evaluated through the removal of turbidity, total suspended solids (TSS), total polyphenols (TPh), and dissolved organic carbon (DOC). The CFD process was demonstrated to be effective in turbidity and TSS reduction in OMW. Using cherry stems (CSs), these reductions were 65.2% of turbidity and 58.0% of TSS, while cherry pits (CPs) achieved higher reductions, 78.6% of turbidity and 68.2% of TSS. To improve the effectiveness of OMW treatment, mainly regarding the removal of TPh and DOC, the CFD process was complemented with the adsorption process (using bentonite clay). The adsorption capacity of bentonite was higher in acidic conditions (pH 3.0) and, with a dosage of 3.0 g L−1, reached 17.3 mg of DOC and 13.8 mg of TPh per gram of bentonite. Several adsorption isothermal models were assessed, and the Langmuir (r2 = 0.985), SIPS (r2 = 0.992), and Jovanovic models (r2 = 0.994) provided the best fittings. According to the optimal operational conditions defined throughout the present work, the combination of CFD and adsorption removals were as follows: (1) 98.0 and 91.3% of turbidity, (2) 80.8 and 81.2% of TSS, (3) 98.1 and 97.6% of TPh and (4) 57.9 and 62.2% of DOC, for CSs and CPs, correspondingly. Overall, the results suggest that cherry by-products can be used as low-cost natural coagulants and, when combined with another natural, abundant, and cheap material, such as bentonite clay, can be a sustainable alternative for treating OMW.