No, but you could carefully configure your scissors so that the cut all happens at once - at the time when the information has travelled the entire length of the system (admittedly, they won’t resemble normal scissors).
It would be conceptually similar to this:
Have a piece of paper 1 light year long - station an infinite number of people along it, each of them instructed to make a tiny cut at a predetermined time after receiving the instruction - the time defined as 1 minus the distance (in LY) from the start.
So I’m the guy at the start and I send out the ‘go’ signal, but because I’m 1 full light year from the other end, I have to wait 1 minus zero years before making my cut - the guy who is a quarter of the way has to wait 1 minus 0.25 years, the guy halfway has to wait 1 minus 0.5 years and so on - all the way to the guy at the very end, who has to wait 1 - 1 years (i.e. he makes the cut as soon as he receives the signal)
-And so in this rather contrived example, everyone cuts at the same time - the cut in the paper ‘travels’ instantaneously from one end to the other, but no infomation can be tagged onto this illusory instantaneous movement, because it’s merely the playing out of something that has already been set in motion.
(I’m pretty sure that other aspects of relativity - the spatial separation and stuff - would complicate the above example, but there’s nothing to stop a cut in paper appearing to move at any speed, because nothing is actually moving at all - it’s just a series of effects.
