Surgical cutting heads for use in infusion/aspiration devices for performing surgery on various parts of the body, are disclosed. These cutting heads include, a first tube, having a cutting edge formed in its proximal end and an inner space bounded by the interior surface of this tube. This first tube contains at least one asymmetrical two-sided notch for cutting tissue, which notch proceeds distally from the first tube's proximal end to an apex where the sides of the notch meet. A first side of the notch commences at the first tube's proximal end and is generally in a plane parallel to the first tube's longitudinal axis. The second side of the notch commences at the first tube's proximal end, at a point radially inwardly therefrom, and extends into the first tube's inner space. A second open tube is disposed concentrically around the first tube and has at least one projection located at its proximal end and extending radially inwardly therefrom overhanging the first tube's proximal end. The interior surface of the second tube is opposed to the exterior surface of the first tube, and the respective opposed surfaces of these tubes define a traversable inner space between the tubes.