If you would like to remove e-mail and URL field from comment form, first uncheck the requirement in Settings > Discussion:
Then add the PHP snippet below to remove the field
add_action( 'after_setup_theme', 'tu_add_comment_url_filter' );
function tu_add_comment_url_filter() {
add_filter( 'comment_form_default_fields', 'tu_disable_comment_url', 20 );
}
function tu_disable_comment_url($fields) {
unset($fields['url']);
unset($fields['email']);
return $fields;
}