Have you looked at your theme's files? You'll likely have to edit the files that come with your theme.
If you go to the administration panel and open the page that is used as your frontpage, then you'd need to check on the right side what template is being used for it. If it says "default template", then you need to go to the directory where WordPress is installed on your server and choose /wp-content/themes/Mystique/ and open page.php or the file that has been specified as the default theme for that page.
In there you'll have something like:
<?php comments_template( '', true ); ?>
If you remove that line, it should not render the comments template anymore.