Welcome to the forum!
I'm curious why you show the cut out object pushed up to just the end of the paper. Is it because that's how a cutter works? I've never actually seen any kind of cutter working. Does it cut things out of a long roll of paper? I've always assumed the paper or card stock, or whatever would be 8.5 x 11 inches (or smaller sometimes, I guess). But I never imagined it would be a long roll of paper.
I like what you've done so far. It's just that the cut out part is so small. To me, it seems like it might be more effective to show something cut out of the whole paper. Or at least half the paper, if you really like sort of a "tail" of paper coming out. If the letter (or whatever) was bigger, it could also have a little bit of a curve. It could actually have the same curve, except the tail end would be sort of raised up relative the the paper.
I wonder if showing the cut out part (the letter or whatever) the same color as the paper, except with a thin border, might help to show the effect? I don't really know if it would help, but it's something I would probably try, at least. It also might help to use a gradient for the "hole", because I guess you could actually see through the hole as it comes out of the machine?? So I wonder if a gradient might help to make that effect?
Yeah, I think I would try to make the hole more black, and the cut out letter more white, like the paper, and maybe with a thin outline.
As for how to do it, Bend LPE seems to be ok, to me. But as Moini mentioned, Pattern Along Path is another way to go. Possiby Envelope Deform LPE, but that would be the last thing I'd try. Bend or PAP should do the job.