Código HTML:
<html>
<head>
<title>Prueba</title>
<script type="text/javascript" src="http://code.jquery.com/jquery-latest.js"></script>
<script type="text/javascript">
$(function (){
$('a').click( function () {
$('#asd option').remove();
});
});
</script>
</head>
<body>
<select name="asd" id="asd">
<option>uno</option>
<option>dos</option>
<option>tres</option>
</select>
<a href="#">Eliminar</a>
</body>
</html>