Ah, figured it out.
In /wp-content/themes/twentyeleven/header.php
, you can comment out this:
// Add the blog description for the home/front page.
$site_description = get_bloginfo( 'description', 'display' );
if ( $site_description && ( is_home() || is_front_page() ) )
echo " | $site_description";
Then the blog tagline won’t be added for the front page.