Remove multiple terms from a post

remove-post-terms.php

<?php

/**
 * Helper function since this function doesn't exist in core
 */
function remove_post_terms( $post_id, $terms_to_remove, $taxonomy ) {
	$terms_to_remove = array_map( 'intval', $terms_to_remove );
	array_filter( $terms_to_remove, function( $term ) { return ! empty( $term ); } );

	// Get the existing terms and only keep the ones we don't want removed
	$current_terms = wp_get_object_terms( $post_id, $taxonomy, array( 'fields' => 'ids' ) );
	$new_terms = array_diff( $current_terms, $terms_to_remove );

	return wp_set_object_terms( $post_id, $new_terms, $taxonomy );
}