The invention provides a moving dredging and flushing device for tunnels and method. The moving dredging and flushing device comprises a trolley, wherein the trolley is erected on trolley guide railsand moves along the trolley guide rails; and a dredging device is arranged on the trolley, is connected to a pressure water pipe and is used for flushing and dredging sediment. The moving dredging andflushing device is also provided with a mud discharge system which comprises a suction pipe, a suction pump and a mud treatment system, wherein the suction pipe is connected to an inlet of the suction pump; and an outlet of the suction pump is connected to the mud treatment system. When the moving dredging and flushing device is used, the trolley is towed to a dredging place, and a mud guard is set; a dredging drill is used for stirring, which cooperates with water current flushing to form mud; the suction pump is started to suck the mud in front of the mud guard into a centrifugal screeningmachine, and particulate matters with the particle sizes of above 3mm are separated out and are discharged to a travelling bogie; the mud of the centrifugal screening machine is transported to a vibrating screen through a slurry pump, and particulate matters with the particle sizes of above 80 micrometers are screened out by the vibrating sieve and are discharged to the travelling bogie; and the sifted mud of the vibrating screen is transported to a mud box, is treated and then serves as flushing water.