Stack Exchange's markdown is just a variation of standard Markdown, so the MultiMarkdown editor may be enough of what you want.
Other options:
MarkdownPad - a "fully featured Markdown editor with live preview". Developed by a SO aficionado.
Emacs Markdown Mode - a plugin for the common programming editor.
See, also, "Are there any text editors which are Markdown aware and provide spell checking features?"
You can always make your own word-processor, that uses Stack Exchange's exact syntax, by wrapping a GUI around Markdown Sharp, which is Stack Exchange's implementation of its custom markdown.