I have a function wp_handle_upload() for uploads files.
$file = $_FILES['attachment_icon-' . $i]; $upload = wp_handle_upload($file, array('test_form' => false));
what is a function for delete a uploaded file?
there is no designated WP function, simply because you already have a PHP one, with the following syntax:
<?php $filename="MyFile.txt" unlink($filename); ?>
for full doc see the PHP manual: