You can get the post ID from the slug with the url_to_postid() function:
$ID = url_to_postid(slug);
then just exclude the ID from your query:
query_posts(array('category_name' => 'Mycat', 'posts_per_page' => -1, 'post__not_in' => $ID ));
You can create an array of post IDs if you need to exclude multiple pages.
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