<!DOCTYPE html>
<html>
<body>
<form>
<select id="mySelect" size="4">
<option>Apple</option>
<option>Pear</option>
<option>Banana</option>
<option>Orange</option>
</select>
</form>
<br>
<button onclick="myFunction()">Remove option with index "2"</button>
<script>
function myFunction() {
var x = document.getElementById("mySelect");
x.remove(2);
}
</script>
</body>
</html>