An apparatus (200) for cutting and applying a component to a tire during a tire building process is disclosed. The apparatus (200) comprises an application head (210) rotatable about a vertical axis and fitted to an X-Y table (220) such that the component (205) can be applied to a curved tire profile spinning on a drum (126, 140) of a tire building machine (100). The application head (210) is configured to feed the component (205) vertically downward to a predetermined position coincident with an intersection of the vertical axis of the application head (210) and a horizontal plane defined by a horizontal axis of rotation of the drum (126, 140) of the tire building machine (100). Also, a method for applying a component to one tire or multiple tires on a tire building machine (100) is disclosed using the apparatus (200).