An apparatus preventing overcharging of a battery and a battery including the apparatus are provided. The apparatus includes holders interposed on respective gaps between battery cells to be stacked and an installation space formed between borders of adjacent holders. A cutting module is inserted into the installation space and an inserted end thereof is disposed between the cells adjacent to an inner side of the installation space to be fixed to a holder and an exposed end thereof has a cutter blade directed to a gap between a lead tap and a bus bar bonded together that is formed. The gap between the ends is connected with a plurality of hinges to compress the hinges to be unfolded when the cell is expanded in a side direction and to deploy the exposed end outwardly for the cutter blade to separate the bonding of the lead tap and the bus bar.