When you minify a file, the result is a completely different file. You need to link it in your page in order to use it.
<script src="site.min.js"></script>
The production version of your index.html file should only link to the minified version and any non-minified version should be removed.
There are gulp plugins which help with this.
They all offer a similar feature where you can specify blocks within HTML comments that will be replaced by the minified version.
<!-- build:js --> <script src="website-module.js"></script> <script src="core.js"></script> <!-- endbuild -->
With the right options within your gulp task, it would become:
<script src="site.min.js"></script>