B/N Co-doped carbon nanosheets (BN-CSs) are considered as the promising candidates for high-performance supercapacitors, yet high-yield preparation of such carbon nanomaterials from a boronate polymer is rarely accessed. Herein, we have demonstrated a possibility of high-yield preparation of BN-CSs by using template-free CuBr2-mediated carbonation of a cross-linked boronate polymer, which is synthesized via a solvothermal polymerization reaction between 4-formylphenylboronic acid and p-phenylenediamine. The effect of activation temperature on the morphology, specific surface area (SBET), heteroatom-doping content, and electrochemial properties of BN-CSs is discussed. It is found that CuBr2, as a mild activation reagent, not only can relieve the over-etching of carbon skeleton and B/N-bearing species, but also can react with the carbon motif via redox reaction mechanism to generate numerous pores. Consequently, the as-prepared BN-CSs present high carbon yield (>52.7 wt%), large SBET value (up to 2714.4 m2 g−1), numerous micorpores coupled with abundant and evenly-distributed B/N species (B > 1.86 at.% and N > 6.26 at.%). All these benefits contribute to the desirable electrochemical performance in both aqueous and ionic-liquid supercapacitors. When 6 M KOH aqueous solution is used as the electrolyte, the BNC-800 electrode delivers a satisfactory capacitance of 258.5 F g−1 at 0.5 A g−1, showing a certain degree of advantages when compared to reported B/N co-doped carbon materials (See Table S4). Moreover, the supercapacitors adopted a ionic-liquid electrolyte achieve a high energy density of 43.7 Wh kg−1 under the power density of 400 W kg−1. These excellent electrochemical properties coupled with both facile polymerization method and versatile CuBr2-activation strategy offer numerous possibilities for further exploration of mass B/N-rich porous polymer and carbon materials, which can be extended to a diversity of functional applications, especially in gas storage, catalysis, and batteries.