Just curious... I'm not in construction and always wondered...
The top sections of the mast beneath the crane are removed one at a time and lowered to the ground. The top section of the crane has hydraulic rams that lower it down one mast section at a time. It is hard to describe without a diagram or photos. See photos at attached link. In some design, the jacking portion is at ground level. The crane jacks itself up so a 20' section of the mast can be unbolted and slide out. Then the jack is lowered so the process can be repeated. See second link for photos and a more detailed explanation.
little pieces by welly chopper