Question: OS X doesn't allow me to cut files. Are there any applications to enable this?

Answer: 
[Path Finder](http://www.cocoatech.com/) supports cutting & pasting files, though I can't think of a case where I'd want to cut & paste that drag & drop wouldn't work.
You can't cut files, but you can:

1. Copy the existing file `⌘C`
2. Delete the existing file `⌘⌫`
3. Paste in the new location `⌘V`

Given that anything you can do with keystrokes can be done by AppleScript, all you would have to do is combine the first two to give you the equivalent of Cut (although you might want to have the script pause a bit between the two…).