The reduction of graphene oxide (GO) by means of thermal and/or chemical treatments leads to the production of reduced graphene oxide (rGO)—a material with improved electrical conductivity and considered a viable and low-cost alternative to pure graphene in several applications, including the production of supercapacitor electrodes. In the present work, GO was prepared by the oxidation of graphite recycled from spent Li-ion batteries using mixtures of sulfuric and phosphoric acids (with different H2SO4/H3PO4 ratios), leading to the production of materials with significant S and P contents. These materials were then thermally reduced, resulting in rGO papers that were investigated by solid-state 13C and 31P nuclear magnetic resonance, along with other methods. The electrochemical properties of the produced rGO papers were evaluated, including the recording of cyclic voltammetry and galvanostatic charge–discharge curves, besides electrochemical impedance spectroscopy analyses. The samples obtained by thermal reduction at 150 °C exhibited good rate capability at high current density and high capacitance retention after a large number of charge–discharge cycles. The results evidenced a strong relationship between the electrochemical properties of the produced materials and their chemical and structural features, especially for the samples containing both S and P elements. The methods described in this work represent, then, a facile and low-cost alternative for the production of rGO papers using graphite recycled from spent batteries, with promising applications as supercapacitor electrodes.