Remove nav menu item by script

Here you go.

//This code will register a Location with wordpress.
//You can assign menu to this location.
add_action('init','register_my_menu');
function register_my_menu(){
    register_nav_menus(array(
        'header_navigation' => 'Header Navigation'
        ));
}

But we haven’t defined any location in theme yet.

This code will be used in theme where you want your menu to get rendered.

<?php

wp_nav_menu($menu_args);
    $menu_args = array(
        'theme_location'=> 'header_navigation', //slug from the previous code.
        'container'     =>  true,   //if you want a div around your menu.
        'menu_class'    => 'nav',   // It will add the class name of menu <ul>
        );
 ?>