Updating an existing comment in the database is done by the function wp_update_comment. As you can see, there is one hook, edit_comment, which you can use to trigger an action when a comment is updated.
However, this hook fires after the comment has been updated. If you want to store the older version of the comment the hook is no use. Also, there is no obvious way to store older versions op the comment. You would have to modify the datastructure, for instance by creating an additional comment metadata field.
You could then hook into the comment_save_pre filter in wp_update_comment to store the old content in that metafield.