It's difficult to say whether "detach" is the most appropriate translation without more context, but, in general, 被 means "the party on the receiving end of the action", as opposed to 加.
So in this case a 加切断物 would be performing the detachment ("detacher") while the 被切断物 would be the target of said detachment ("detachee").
The most obvious example is 被害者 Vs. 加害者.

Japanese term (edited): 被切断物

A workpiece is a piece of raw material that is in the process of being formed into a component or part.


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Note added at 2 days 21 hrs (2019-09-09 12:13:42 GMT)
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However, if as Lekhika specifies, the cutting is done with a plasma jet onto a metal sheet, we can expect the contour of the cut-out obtained to be anything but rectilinear from start to finish; in which case one way to make such a complex cut is by having the workpiece clamped on a moving tray the X,Y and combined X-Y movements of which are governed by an numerically controlled program, with the plasma jet nozzle remaining in the fixed position, as seems to be the case here. Now if the workpiece were much too heavy and large for being moved around, we could expect the reverse option to be adopted, with the workpiece being fixed and the NC program governing the
displacements of the much lighter plasma nozzle with its flexible supply cabling.