A Device for producing cuts or perforations on a human or animal eye at the anterior or posterior opening of the eye lens (capsulatomy, rhexis) with a cutting element that can be inserted into the interior of the eye and a drive device which is arranged outside of the eye in order to cause movement, in particular oscillatory vibrations or rotation of the cutting element inside the interior of the eye, the drive device having a field generator for generating a magnetic or electromagnetic excitation field and the cutting element can be excited, in particular driven, by way of the excitation field generated by the field generator.