Removing My Sites menu from Admin

You can use remove_submenu_page to remove it. Note that it doesn’t prevent visiting that page if you manually enter the URL.

function adjust_the_wp_menu() {
    $page = remove_submenu_page( 'index.php', 'my-sites.php' );
}
add_action( 'admin_menu', 'adjust_the_wp_menu', 999 );

Based on the example from remove_submenu_page Codex page.