Abstract: Cutting assembly comprising a blade or two half-cutting blades (40a, 40b) each composed of a point (43, 43a, 43b) of generally triangular form, located in a plane forming substantially a right-angle with a reference plane P, a sole (42, 42a, 42b) of given length (r), located in a plane substantially parallel to the reference plane P, and a cutting edge (41, 41a, 41b) located in a plane forming a given acute angle (?) with the reference plane P. Assembly process intended for the production of tires, comprising a cutting device enabling sets of pre-assembled profiled elements to be cut and for joints to be produced by superposition in which the products of the same nature are superposed directly on one another.