An oblique fastening apparatus includes a positioning unit and a clamping unit capable of moving relatively. The positioning unit includes a positioning base, a positioning guide piece, a positioning piece and a first oblique fastening channel penetrating through the positioning guide piece and the positioning piece in an inclined manner. The first oblique fastening channel is provided with a first chip removal segment exposed between the positioning guide piece and the positioning piece. The clamping unit includes a clamping base capable of moving relative to the postioning base and a clamping piece. By the design of the positioning base and the clamping base capable of moving relatively, the apparatus is suitable of a plurality of clamp tool capable of driving the positioning base and the clamping base to move relatively, so that the application range is wide and the clamping force and stability can be improved. Besides, the first chip removal segment exposed between the positioning guide piece and the positioning piece can enable the residual chip to discharge quickly so as to aovid blocking.