A tilting device for cropping a sheet of laminated glass, comprising two side-by-side rows of suckers, each supported by a bar of a frame which is pivoted, on the opposite side with respect to the suckers, to a supporting structure, the bars both resting on the same elements for the alternating lifting and lowering of the bars, which are adapted to produce the simultaneous alternating tilting of both of the frames and of the corresponding rows of suckers.