The invention discloses a multi-stage fixed-wing underreamer, comprising a cylindrical body. Blade wings are uniformly distributed circumferentially on the cylindrical body; each blade wing is provided with at least two stages of cutting wings which are expanded gradually from bottom to top, the diameter of the first stage of cutting wing at the bottom is greater than that of an open well, and thediameter of the biggest stage of cutting wing at the top is equal to the designed wellhead diameter; back-slide teeth are arranged at the upper end of one lateral side of each blade wing while cutting teeth are arranged at the middle lower part of the lateral side of the blade wing; protective alloy pins are arranged on the outer circumference of each cutting wing. The invention further disclosesa method for reaming before soft formation pilot hole side drilling by utilizing the multi-stage fixed-wing underreamer. The underreamer reams the bore holes gradually, is not easy to tilt under guide of a guide shoe, and thus, quality of reaming before soft formation pilot hole side drilling is guaranteed; since the reaming can be completed by one-step work, construction efficiency of reaming before soft formation pilot hole side drilling is improved.