A modular unit configured for mounting to a cutting head of a slicing machine and for securing a knife to the cutting head, and slicing machines equipped with one or more of such modular units. The modular unit includes mounting blocks adapted to be spaced apart in an axial direction of the cutting head, and a clamping assembly assembled with the mounting blocks so as to extend between the mounting blocks. The clamping assembly is configured to secure a knife to the cutting head, and at least portions of the clamping assembly may be removable from the cutting head by disassembling the clamping assembly from the mounting blocks without removing the mounting blocks from the cutting head.