Cacher is the code snippet organizer for pro developers

add_filter('posts_clauses', 'posts_clauses_with_tax', 10, 2);
function posts_clauses_with_tax( $clauses, $wp_query ) {
	global $wpdb;
	//array of sortable taxonomies
	$taxonomies = array('example-taxonomy', 'other-taxonomy');
	if (isset($wp_query->query['orderby']) && in_array($wp_query->query['orderby'], $taxonomies)) {
		$clauses['join'] .= "
			LEFT OUTER JOIN {$wpdb->term_relationships} AS rel2 ON {$wpdb->posts}.ID = rel2.object_id
			LEFT OUTER JOIN {$wpdb->term_taxonomy} AS tax2 ON rel2.term_taxonomy_id = tax2.term_taxonomy_id
			LEFT OUTER JOIN {$wpdb->terms} USING (term_id)
		";
		$clauses['where'] .= " AND (taxonomy = '{$wp_query->query['orderby']}' OR taxonomy IS NULL)";
		$clauses['groupby'] = "rel2.object_id";
		$clauses['orderby']  = "GROUP_CONCAT({$wpdb->terms}.name ORDER BY name ASC) ";
		$clauses['orderby'] .= ( 'ASC' == strtoupper( $wp_query->get('order') ) ) ? 'ASC' : 'DESC';
	}
	return $clauses;
}