JSFiddle - React, Tailwind, and code Playground

HTML

<form class="form-horizontal well" method="post" action="/cgi-bin/dropdown.py">
    <fieldset>
      <legend>Select Audit Point</legend>

      <div class="control-group">
        <label class="control-label" for="select01">Select Tier</label>
        <div class="controls">
          <select id="select01" name="select01">
            <option value="All Tier">All Tiers</option>
            <option value="Database Tier">Database Tier</option>
            <option value="Application Tier">Application Tier</option>
            <option value="Web Tier">Web Tier</option>
          </select>
        </div>
      </div>

      <div class="control-group">
        <label class="control-label" for="select01">Select Version</label>
        <div class="controls">
          <select id="select02" name="select02">
            <option value="Oracle" name="Oracle">Oracle</option>
            <option value="SQL" name="SQL">SQL</option>
            <option value="Both" name="Both">Both</option>
          </select>
        </div>
      </div>

      <div class="control-group">
        <label class="control-label" for="select01">Select Audit Point</label>
        <div class="controls">
          <select id="select03" name="select03">
            <option class="All Tiers" value="Eagle Software Version">Eagle Software Version</option>
            <option class="All Tiers" value="Server OS, Memory, CPU">Server OS, Memory, CPU</option>
            <option class="All Tiers" value="High Availability">High Availability</option>
            <option class="Database Tier" value="DBMS Version">DBMS Version</option>
            <option class="Database Tier" value="DBMS Statistics">DBMS Statistics</option>
            <option class="Database Tier" value="DBMS Parameters">DBMS Parameters</option>
            <option class="Database Tier" value="DBMS Data File Growth">DBMS Data File Growth</option>
            <option class="Database Tier" value="Database Disk Structure">Database Disk...

JavaScript

var savedOptions = '';

        savedOptions = $('#select03').html(); //save the second dropdown-list

        $('#select01').change(function() {
            var selectedValue = $('#select01').val(); //After changing the value of the first dropdown, store this value inside a variable

           $('#select03').html(savedOptions); //restore the content of the 2nd dropdown
            $('#select03').children('option').each(function() {
                if(!$(this).hasClass(selectedValue)) {
                    $(this).remove(); //Compare and step through the 2nd dropdown and delete all unneccessary options
                }
            });
        });