En donde 123 es el ID del post a eliminar.

RESTAPI_borrado_entrada.php

<?php
$host = 'http:/tudominio.com/wp-json/wp/v2/posts/123';

$headers = array(
    'Content-Type:application/json',
    'Authorization: Basic '. base64_encode('admin:clave')
);
$ch = curl_init($host);
curl_setopt($ch, CURLOPT_HTTPHEADER, $headers);
curl_setopt($ch, CURLOPT_CUSTOMREQUEST, 'DELETE');  
curl_setopt($ch, CURLOPT_RETURNTRANSFER,1);
$result = curl_exec($ch);
curl_close($ch);  
echo($result);