Remove auto added <p> from a page that has no literal content (uses shortcodes)

There are a few things you can try.

You can pospone the wp_autop because it processes before the shortcode output:

remove_filter( 'the_content', 'wpautop' );
add_filter( 'the_content', 'wpautop' , 12);

Or use the cleanup_shortcode_fix() function that should help with your issue:

function cleanup_shortcode_fix($content) {
    $array = array('<p>[' => '[', ']</p>' => ']', ']<br />' => ']', ']<br>' => ']');
    $content = strtr($content, $array);
    return $content;
}

add_filter('the_content', 'cleanup_shortcode_fix');
$string = preg_replace_('/<p>s*</p>/', '', $string);
add_filter('the_content', 'cleanup_shortcode_fix', 1);

There are various functions aside from wpautop() that filter post content, such as force_balance_tags(), which was designed to balance bad HTML coming in via the editor.

They're mostly defined in formatting.php, where you can see the various code in source.

Removal of these filters can be as simple as one line, as you point out:

remove_filter('the_content', 'wpautop');

For more information: http://codex.wordpress.org/Function_Reference/wpautop

Check out below links which will help you.

1. Removing <p> and <br/> tags in WordPress posts
2. wordpress-wrapping-shortcodes-with-p-tags
3. Disable wpautop Plugin

may this help you.

Try this(paste this code somewhere in functions.php):

function shortcode_empty_paragraph_fix($content){   
    $array = array (
        '<p>[' => '[', 
        ']</p>' => ']', 
        ']<br />' => ']'
    );

    $content = strtr($content, $array);
    return $content;
}

add_filter('the_content', 'shortcode_empty_paragraph_fix');