A mechanism for twisting off a drill rod includes a front clamping body (J0) and a rear clamping body (J1) both of which are installed at a fixed bracket. Each of the front clamping body (J0) and the rear clamping body (J1) includes a positioning clamping device and a clamping execution device which are respectively installed at two sides of a clamping centerline (JC) and opposite to each other. The front clamping body (J0) is installed within the first fixed bracket element (80) through a rear fixed shaft. The rear clamping body (J1) is installed within an overturn bracket (6) of the second fixed bracket element (81) through a rear fixed shaft. The positioning clamping device and the clamping execution device of both the front clamping body (J0) and the rear clamping body (J1) are asymmetric to each other.