A snivel removing device includes a housing having a partition to form two chambers and an outlet port and an inlet port communicating with the chambers. One or more bladders are attached to the housing, and communicating with the chambers, and compressible and expandable to draw the snivel into one of the chambers of the housing via the inlet port, and then into the other chamber of the housing, and to flow out through the outlet port of the housing. Two or more check valve may be used to control the flowing of the snivel. An arm is attached to each bladder, and an operating device may operate the arm to depress and to expand the bladder.