The invention relates to a machine and process for grinding dies, in which the work axis (CO) of the plate (2.1) in which the die (1) to be machined is anchored is controlled at all the points of its angular movement, allowing the interpolation of the movements of this work axis (CO) with those of an axis of rotation (BO) and with those of respective axes (X and Z), such that the machines has four axes of interpolation, which allows machining dies (1) with their inner or outer diameter rounded or non-rounded and with their transition between these diameters and the side faces constant or variable by means of a single grinding process.