Abstract: The present disclosure relates to the field of display technologies, and provides an abutment, a laser cutting device and a control method thereof, so as to improve the yield rate and prolong the service life of a product. Specifically, the abutment comprises a carrying region. The carrying region is used for placing a component to be cut thereon, and comprises an adsorbing region and a cutting region. Furthermore, the adsorbing region is provided with adsorbing holes for adsorbing the component to be cut. Besides, the cutting region extends from a side of the carrying region to an opposite side thereof.