An apparatus for cutting a tissue part of an eye by means of laser radiation includes a suction-ring unit (16) which is capable of being mounted onto the eye, with a ring axis (22), a mechanical interface unit (34) which is separate from the suction-ring unit (16), which is capable of being moved along the ring axis (22) in coupling contact with the latter, and which is capable of being mechanically coupled with optical means (70) which focus the laser radiation onto or into the tissue part (12) of the eye, and sealing means (44, 52) which upon movement of the interface unit (34) in coupling contact with the suction-ring unit (16) form a space (58) which is capable of being evacuated and which is delimited by sealing surfaces (46, 60) of the interface unit (34) and of the suction-ring unit (16) and of the sealing means (44, 52).