$term_name = 'Upcoming'; //category to delete
$taxonomy = 'category'; //type of taxonomy to be changed
$term = get_term_by('name',$term_name, $taxonomy);
$args='';
$old_terms = wp_get_post_terms( $post_id_to_update, $taxonomy, $args );
$new_terms = array();
if ($old_terms) {
    foreach ( $old_terms as $old_term ) {
        if ($old_term->term_id != $term->term_id) {
            $new_terms[]=$old_term->term_id;
        }
    }
}
wp_set_post_terms( $post_id_to_update, $new_terms, $taxonomy, $return );