Deletes a specified menu item from all sites on all networks on a WordPress multisite.

deleteMenuItem.php

<?php

// Script must be run with wp eval-file
if(!defined('ABSPATH')){
    die('You shall not pass.');
}

class DeleteSpecifiedWordPressMenuItem {

    protected $menuNameToBeDeleted;
    protected $menuNames;
    protected $networks;

    public function __construct()
    {
        $this->menuNameToBeDeleted = "About Me";
        $this->menuNames = ['Header Navigation', 'Footer Navigation'];
        $this->networks = get_networks();
    }

    public function deleteMenuItem(){
        foreach($this->networks as $network){
            $sites = get_sites(['network_id' => $network->id]);
            foreach($this->menuNames as $menuName){
                foreach($sites as $site) {
                    $url = $site->domain . $site->path;
                    $output = shell_exec("wp menu item list '" . $menuName . "' --url=$url");
                    $array = explode("\n", $output);
                    $matches = preg_grep("/$this->menuNameToBeDeleted/", $array);
                    if($matches){
                        $match = array_shift($matches);
                        $pieces = explode("\t", $match);
                        $deletedOutput = shell_exec("wp menu item delete $pieces[0] --url=$url");
                        printf(str_replace(".\n", "", $deletedOutput) . " for $menuName in $url\n");
                    } else {
                        printf("No matches found for $menuName in $url\n");
                    }
                }
            }
        }

    }

}

$object = new DeleteSpecifiedWordPressMenuItem();
$object->deleteMenuItem();