The invention relates to a tobacco cutting machine cutter which comprises a cutter roll body, a fixing-holding mechanism mounted on the surface of the cutter roll body and a ceramic cutter blade fixed between the fixing-holding mechanism and the cutter roll body. A plurality of mounting surfaces are arranged on the side face of the cutter roll body; the fixing-holding mechanism is located on the mounting surfaces and fixedly connected with the cutter roll body; one end of the ceramic cutter blade is located between the fixing-holding mechanism and the mounting surfaces; and the other end of the ceramic cutter blade exposes out of the cutter roll body and the fixing-holding mechanism for cutting tobacco. The tobacco cutting machine cutter adopts the ceramic cutter blade, the structure is simple, abrasion resistance is achieved, and the tobacco cutting efficiency is high. The invention further relates to cutter grinding equipment provided with the fixing-holding mechanism and used for dressing the ceramic cutter blade and increasing the cutter replacing speed.