If I'm reading your question right, you're dealing with a string, not with elements, so you can use String#replace:
theString = theString.replace(/<option[^>]*>([^<]+)<\/option>/g, "$1");
replace looks for special sequences in the replacement string, and fills them in from information on the matched occurrence. In this case, I'm using a capture group to capture the bit between <option...> and </option>, then using $1 to replace the overall match with the content of the first capture group.
Complete example: Live Copy *(I've added <br> between them just for output purposes):
<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8">
<title>Example</title>
</head>
<body>
<script>
(function() {
"use strict";
var theString =
'<option value="AU">Australia</option><br>' +
'<option value="AT">Austria</option>' +
'<br><option value="AZ">Azerbaijan</option>' +
'<br><option value="BS">Bahamas</option>' +
'<br><option value="BH">Bahrain</option>' +
'<br><option value="BD">Bangladesh</option>';
theString = theString.replace(/<option[^>]*>([^<]+)<\/option>/g, "$1");
display(theString);
function display(msg) {
var p = document.createElement('p');
p.innerHTML = String(msg);
document.body.appendChild(p);
}
})();
</script>
</body>
</html>
<option>elements? And put them where?