To catch a back-wind fiber in a short time by moving a cutting mem ber along the axis of a bobbin on which the back-wind fibers is wound.

A helical back-wind fiber (y) rotates a tray (t) in the direction toward a cutting edge 15g and positioning a sliding member 8 near the top end of a fine spinning bobbin (p). An air cylinder is operated to turn a cutter mounting member 13 mounted on a cylindrical member 12 around a supporting column 6a such a that a cutting member 15 comes into contact with the fine spinning bobbin (p). Next, when a vertical cylinder is operated to move down the sliding member 8, the cutting member 15 is turned down while being in contact with the rotating fine spinning bobbin (p) and reliatably rapidly catch the back-wind fiber (y). The down-movement of the sliding member 8 is stopped and the cutter mounting member 13 is rapidly turned by the cutting member 15 is an direction separated from the fine spinning bobbin (p), thereby reliably cutting the back-wind fiber (y).