unset($a->new_property);
This works for array elements, variables, and object attributes.
Example:
$a = new stdClass();
$a->new_property = 'foo';
var_export($a); // -> stdClass::__set_state(array('new_property' => 'foo'))
unset($a->new_property);
var_export($a); // -> stdClass::__set_state(array())