A device includes a digging device to cut the seafloor and with a device for hooking onto a pipeline and for sliding over the same. The device includes at least one float device constrainable to the pipeline for supporting it in span, connected to the back of said digging device with respect to the direction of the movement. The method includes excavating the seafloor by a digging device, collecting a float device from a storage base and transporting it to said pipeline, constraining the first float device to the pipeline behind the digging device and connecting the first float device to the digging device, when at least one portion of pipeline is in a suspended configuration, and when the portion of suspended pipeline increases, collecting a subsequent float device and constraining it to the pipeline and connecting the same to the float device previously constrained.