How would I use DATEDIFF(), NOW(), and BETWEEN in a db_delete() query?
You can use DeleteQuery::where(), e.g.

$args = array(':arg1' =&gt; $foo, ':arg2' =&gt; $bar);
db_delete('note_dates')
  -&gt;where("DATEDIFF('start', NOW()) BETWEEN :arg1 AND :arg2", $args);
  -&gt;execute();


That'll give you

DELETE FROM {note_dates} 
WHERE  (DATEDIFF('start', NOW()) BETWEEN :arg1 AND :arg2)