A vitreous cutter for use in removing vitreous from the eye during intraocular surgery. The cutter includes an outer tube (1,52,81) having a side-facing opening (6,52,82) with a perimeter edge forming a cutting blade (52a). An inner tube (2,50,80) is received coaxially in the outer tube and is provided at one end with a side facing opening (5) whose perimeter edge forms a second cutting edge (5A,58a,88a). The inner tube (2,50,80) is rotatable about its axis relative to the outer tube (1,52,81) to cause the side facing openings (5,6,52,82) to alternately rotate into and out of alignment. This causes the cutting edges (5A,52a,58a,88a) to sever vitreous sucked into the aligned openings by suction pressure applied to the opposite end of the inner tube. Relative rotation of the two tubes is caused by an air-driven reciprocating piston (3) having a rack (11) that engages a pinion (9) attached to the inner tube.