PURPOSE: To improve the delivery handling of fragments by installing a fragment holding member free of movements in space between the neighborhood of a cutting position and a position out of the conveying area of a cut work, in a fragment holder in a sewing machine or the like.

CONSTITUTION: When a workpiece W is subjected to trimming by a band sawblade 21, and a sawblade housing 5 turns to an up motion from a down end by a lifting cylinder, a front fragment work WA goes up together by operation of a one-way clutch of a press roller 35a. When the sawblade housing 5 reaches the upper end, a support arm 59a rocks in the horizontal direction, having a work holder 61a situated in the neighborhood of a cutting position from the conveying area. Next, the front fragment work WA is held between an upper jaw 63a and a lower jaw 67a, releasing the pressing force of the press roller 35a, and the work holder 61a is horizontally rocked by the support arm 59a, thereby taking out it to the left of the conveying area.