Provided is a small multi-assembly brazing clamping device. The small multi-assembly brazing clamping device comprises cores, wherein an upper supporting board is installed on a cover board at the tops of the cores, a lower supporting board is installed on a cover board at the bottoms of the cores, an upper base board is installed at the top of the upper supporting board, a lower base board is installed at the bottom of the lower supporting board, the two sides of the upper base board and the two sides of the lower base board are respectively provided with a plurality of through holes, and screws are installed in the through holes and are perpendicular to the upper base board and the lower base board respectively; the head portions of the screws are fixed on the top of the upper base board through first nuts, the bottoms of the screws are fixed at the upper end of the lower base board through second nuts, and the bottoms of the screws are fixed at the lower end of the lower base board through third nuts. The cores are installed between the upper base board and the lower base board, and the screws which are perpendicular to the cores are installed, so that the phenomenon of dislocation of the cores when thermal expansion stress occurs in the brazing process is prevented; the head portions and the root portions of the screws are respectively fixed on the base boards through the nuts, so that the structure is firm, the shifting phenomenon does not happen, the perpendicularity of the cores is guaranteed, and accordingly the brazing quality of the cores is ensured.