Disable Link to Post from Showing Up in Post’s Comments?

It sounds like you’re talking about a pingback. You can disable it from Admin|Settings|Discussion. Uncheck Attempt to notify any blogs linked to from the article.

Or, you can do it on a post-by-post basis under “Discussion” below the post you’re creating/editing. You might need to enable “Discussion” in the “Screen Options” menu at the top of the page.