Gidpoiiohika,
<!DOCTYPE html>
<html>
<head>
<title>Untitled</title>
<meta charset="utf-8">
<style type="text/css">
</style>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.12.4/jquery.min.js"></script>
<script>
$(function() {
$(".form-control").change(function() {
var i = this.selectedIndex;
this.options.remove(i);
})
});
</script>
</head>
<body>
<select class="form-control js-category-select" name="project[categories_projects_attributes][1543933181636][category_id]" id="project_categories_projects_attributes_1543933181636_category_id">
<option value="">Select Category</option>
<option data-default_external_rate="0" value="5">Management</option>
<option data-default_external_rate="0" value="7">DevOps</option>
<option data-default_external_rate="0" value="8">Design</option>
</select>
<select class="form-control js-category-select" name="project[categories_projects_attributes][1543933186714][category_id]" id="project_categories_projects_attributes_1543933186714_category_id">
<option value="">Select Category</option>
<option data-default_external_rate="0" value="5">Management</option>
<option data-default_external_rate="0" value="7">DevOps</option>
<option data-default_external_rate="0" value="8">Design</option>
</select>
</body>
</html>