Vitrectomy is an ophthalmic microsurgical procedure that removes part or all of the vitreous humor from the eye. The procedure uses a vitreous cutter consisting of a narrow shaft with a small orifice at the end through which the humor is aspirated by an applied suction. An internal guillotine oscillates back and forth across the orifice to alter the local shear response of the humor. In this work, a computational study of the flow in a vitreous cutter is conducted in order to gain better understanding of the vitreous behavior and provide guidelines for a new vitreous cutter design. The flow of a Newtonian surrogate of vitreous in a two-dimensional analog geometry is investigated using a finite difference-based immersed boundary method with an algebraically formulated fractional-step method. A series of numerical experiments is performed to evaluate the impact of cutting rate, aspiration pressure, and opening/closing transition on the vitreous cutter flow rate and transorifice pressure variation during vitrectomy. The mean flow rate is observed to increase approximately linearly with aspiration pressure and also increase nearly linearly with duty cycle. A study of time-varying flow rate, velocity field, and vorticity illuminates the flow behavior during each phase of the cutting cycle and shows that the opening/closing transition plays a key role in improving the vitreous cutter’s efficacy and minimizing the potential damage to surrounding tissue. The numerical results show similar trend in flow rate as previous in vitro experiments using water and balanced saline solution and also demonstrate that high duty cycle and slow opening/closing phases lead to high flow rate and minor disturbance to the eye during vitrectomy, which are the design requirements of an ideal vitreous cutter.