The invention discloses a cutter of a shield tunneling machine. The cutter is used for cutting an underground consolidated drainage plate and braided fabric. The cutter comprises a cutter body, a cutter bit and a cutter bit sharp edge; the cutter bit is inlaid in the head part of the cutter body; the tool bit sharp edge is inlaid on the cutter bit; the height of the tool bit sharp edge is larger than the preset height; a cutting edge included angle of the cutter bit sharp edge is smaller than a preset angle; the cutter bit sharp edge is provided with three surfaces; and the side surface of thecutter bit sharp edge is in an inverted trapezoid shape. According to the cutter of the shield tunneling machine, the cutter bit sharp edge preferentially cuts the interior of a soil body, the consolidated drainage plate and the braided fabric in the soil body are cut firstly, the cutter bit then performs tearing, damaging and tunneling on the soil body, so that the effect of cutting the consolidated drainage plate and the braided fabric into sections can be achieved, the winding effect of the drainage plate and the braided fabric on a cutterhead can be reduced, the consolidated drainage plate, the braided fabric and muck can be conveniently removed, and therefore the tunneling efficiency of the shield tunneling machine is improved. The invention further discloses the cutterhead of the shield machine using the cutter, and further discloses a method for cutting the consolidated drainage plate for the shield tunneling machine by using the cutterhead.