The invention discloses a device and method for treating mud-containing acid water so as to solve the problem of an existing treatment device that the solid content of supernatant is high, which leads to deposition of acid mud easily. The treatment device comprises a torrential rinsing tower, a cooling tower, a clear liquid tank, a cooling tower slurry pump, a torrential rinsing tower slurry pump and a plate-and-frame filter press. The torrential rinsing tower, the cooling tower and the clear liquid tank are communicated with each other. The outlet end of the cooling tower is connected with the torrential rinsing tower through the cooling tower slurry pump, one path of the outlet end of the torrential rinsing tower is connected with the plate-and-frame filter press through the torrential rinsing tower slurry pump, the outlet end of the plate-and-frame filter press is connected with the clear liquid tank, and another path of the outlet end of the torrential rinsing tower returns to the torrential rinsing tower through the torrential rinsing tower slurry pump. The device is simple to operate, small in investment and low in energy consumption, continuous mud removal of the mud-containing acid water in a purification process is performed, the deposition of the acid mud in each purification tower is avoided, the solid content of clear liquid formed after filter-press treatment of the mud-containing acid water is below 0.05 g/l, and a flue gas cooling and dedusting effect is improved.