The invention discloses a construction method for a cement gypsum composite stable steel slag base layer. The construction method comprises the steps of construction preparation, construction lofting, centralized mixing of a mixture, mixture transportation, mixture paving by a paver, mixture compaction forming, quality inspection, watering maintenance, traffic control, handover inspection and the like. The invention also discloses a paver which comprises a paving mechanism, a measuring mechanism, a cutting mechanism and a cleaning mechanism; and the measuring mechanism is arranged at the rear end of the paving mechanism, the cutting mechanism is arranged at the rear end of the measuring mechanism, and the cleaning mechanism is arranged at the front end of the paving mechanism. According to the paver, transverse joint treatment is facilitated, follow-up connection is facilitated, the paving thickness can be rapidly measured, impurities on a road surface can be cleaned, and the road surface can be kept wet. The desulfurized gypsum and the steel slag are solid wastes of iron and steel enterprises, environmental pollution caused by the solid wastes of the enterprises is reduced, natural environment damage caused by collection of highway construction aggregates is reduced, and the method is more ecological and environment-friendly compared with a traditional process and has social and economic benefits.