A hair cutting appliance includes a mounting unit configured to couple a cutting unit to a housing. The mounting unit includes a swivel mechanism having a base portion configured to be coupled to the housing, and a top portion configured to be coupled to the cutting unit, where the base and top portions are movable with respect to each other, such that, during operation, the cutting unit is pivotably supported by the swivel mechanism, which defines a virtual pivot axis for the cutting unit. The virtual pivot axis is substantially parallel to a cutting edge of the cutting unit. In a first or shaving state of the swivel mechanism, the virtual pivot axis is located at a first position with respect to the cutting unit, and in a second or styling state, the virtual pivot axis is located at a second position that is different from the first position.