In a world where an eco-friendlier approach is becoming more and more necessary, it is essential to reduce waste production and to reuse residues of the company’s supply chain. Coffee silverskin (CS) and spent coffee ground (SCG), two by-products of coffee production, are important sources of bioactive compounds and, for this, some authors have proposed their reuse in the nutraceutical, food, and cosmetic sector. However, their potential enzyme inhibitory properties have been poorly investigated. Hence, the objective of the current work was to study the enzymatic inhibitory activities against acetylcholinesterase, butyrylcholinesterase, α-amylase, α-glucosidase, and tyrosinase of different extracts of CS and SCG. Before these in vitro bioassays, the phytochemical composition of each extract was investigated via colorimetric assays and HPLC-MS/MS analysis. In addition, the antioxidant activities were evaluated by different chemical approaches. SCG extracts contained a higher content of bioactive compounds, notably the SCG EtOH:H2O extract was the richest in caffeine and possessed the highest antioxidant activities. The hydroalcoholic and methanolic extracts were shown to be the most active against all tested enzymes, while the water extracts displayed lower activity. Our results showed a weak correlation between bioactive compounds and enzyme inhibitory effects, proving inhibitory activities likely due to non-phenolic molecules such as alkaloids and terpenoids. Obtained findings could be a starting point to develop novel nutraceuticals from CS and SCG.