"get_the_terms" to the order of the "term_order". (order by ASC.)

get_the_terms_orderby_termorder.php

<?php
/*==================================================
	"get_the_terms" to the order of the "term_order". (order by ASC.)
================================================== */
function get_the_terms_orderby_termorder($taxonomy){
	global $post;
	$terms = get_the_terms($post->ID, $taxonomy);
	$array = array();
	foreach($terms as $term){
	        $array[$term->term_order] = (object)array(
	            "term_id"          => $term->term_id,
	            "name"             => $term->name,
	            "slug"             => $term->slug,
	            "term_group"       => $term->term_group,
	            "term_order"       => $term->term_order,
	            "term_taxonomy_id" => $term->term_taxonomy_id,
	            "taxonomy"         => $term->taxonomy,
	            "description"      => $term->description,
	            "parent"           => $term->parent,
	            "count"            => $term->count,
	            "object_id"        => $term->object_id
	        );
	}
	ksort($array);
	$array = (object)$array;

	return $array;
}
?>

<?php
/*==================================================
	▼Usage Example (Get the slug)
================================================== */
$orderterms = get_the_terms_orderby_termorder("mytaxonomy");
if($orderterms){
	foreach($orderterms as $term){
		echo $term->slug;
	}
}
?>