I did wonder how you did that, cut a document from one computer then paste it into another, but I have just tested this on my home network, (2 PCs), and it is possible.
Using the mouse on the same computer for both actions I cut a txt file from one computer and pasted it into the other.
Once I did that and closed the connection, it had gone from the source computer.
If you did the identical procedure, then the same applies.
However, if you moved this file to some interim media, eg a memory stick, CD or similar, is it still on that media?
You can try the other software recovery utilities suggested in the thread below, but I would not be too hopeful;
I assume you had no backups.
Is this possible, or is it lost forever? The problem is that the pc that it was paste to, is gone (sold), and we lost an important document. I've tried Pandora Recovery, but with no result.