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

Answer: 
It *is possible* to cut-paste files/folders in OSX 10.7 Lion's Finder (so, since 2011), but the OSX way is *slightly* different from the Windows way.

1. `⌘`-`C` (copy first)
2. `⌘`-`⌥`-`V` (now *move* to it's destination)

So, the steps are very similar to copy-paste, but holding `⌥` (option key) moves the file/folder instead of copies it.

You can also have a look in the edit menu after copying a file - press `⌥` while looking to see the difference: "paste" changes to "move item here".
[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.