The invention relates to a device of a boiling chlorination furnace for continuous slagging and a slagging method. The device is formed by a slagging pipe, a slagging valve, a water cooling spiral deslagging machine and a slagging tank that are sequentially connected through pipelines, the slagging valve comprises a vertical tube and a material discharge chamber that are in parallel, the material discharge chamber is communicated with the vertical tube through a hole at the bottom of the material discharge chamber, a material discharge opening is arranged at the upper part of the material discharge chamber, and the vertical tube and the bottom of the material discharge chamber are respectively provided with an air inlet. Slag forms stock columns in the vertical tube so that the device automatically seals, therefore, gas in the boiling chlorination furnace is prevented from leaking, slagging discharge rate is controlled through nitrogen flow regulation, and regulation and control of chlorination slagging rate are realized. According to the device, the boiling chlorination furnace realizes continuous slagging through a sealing and controllable manner without using a mechanical valve, therefore, the chlorination furnace is effectively prevented from leaking gas in the slagging process. The device has the advantages of being good in sealing performance, simple in operation, safe and reliable, easy to realize automatic control and the like.