A mechanical disc brake structure contains: a body, a brake set, and a drive unit. The body includes two clamp seats between which an accommodation space is defined so as to accommodate a circular disc. The brake set contains: a rotation member includes a coupling column, a rotatable block, and a connection portion. The rotatable block has a push face, the rotation member includes a through aperture, and the stop fringe has a first retaining portion. The engagement member includes a braking disc having a forced face and a shaft. The shaft has a second retaining portion and a threaded orifice. An actuation structure is defined between the push face and the forced face. A torsion spring is accommodated in the through aperture. A screw element is screwed with the threaded orifice, and a locking member is locked with the rotation member.