JSFiddle - React, Tailwind, and code Playground

HTML

<select id="Questions1">
    <option value="1">Option 1</option>
    <option value="2">Option 2</option>
    <option value="3">Option 3</option>
</select>
<select id="Questions2">
    <option value="1">Option 1</option>
    <option value="2">Option 2</option>
    <option value="3">Option 3</option>
</select>

JavaScript

// Build a javascript array with all of the select names/values
var options = new Array();
$('#Questions1 option').each(function() {
    $this = $(this);
    options.push({ Name: $this.text(), Value: $this.val() });
});

// Create a function for re-building a select minus the chosen option
var rebuildSelect = function($selOption, $select) {
    $previouslySelected = $select.find(':selected');
    $select.empty();
    for (var i = 0; i < options.length; i++) {
        var opt = options[i];
        if (opt.Value != $selOption.val()) {
            if ($previouslySelected.val() == opt.Value) {
                $select.append('<option value="' + opt.Value + '" selected="selected">' + opt.Name + '</option>');
            }
            else {
                $select.append('<option value="' + opt.Value + '">' + opt.Name + '</option>');
            }
        }
    }
}

// Wire up the event handlers
var $Questions1 = $('#Questions1');
var $Questions2 = $('#Questions2');

$Questions1.change(function() {
    rebuildSelect($(this), $Questions2);
});

$Questions2.change(function() {
    rebuildSelect($(this), $Questions1);
});

// Go ahead and run the function once to remove the default entry from the second box
rebuildSelect($Questions1.find(':selected'), $Questions2);