A device (1) for cutting an ophthalmic lens (L1) to be mounted onto a spectacle frame, includes: elements (10) for locking and rotating the ophthalmic lens about a locking axis (A1); a tool holder which supports at least one first tool (60) rotatable about a rotational axis (A2) and a second tool (80) rotatable about a finishing axis (A6) and which has a spacing mobility (ESC) for the spacing apart thereof from the locking axis, a shifting mobility (TRA) for the axial positioning thereof along the locking axis, and a pivoting mobility (PIV) for adjusting the orientation of the rotational axis relative to the locking axis; and elements for controlling the three mobilities of the tool holder. The rotational and finishing axes are separate from one another.