In Drupal 7, this can be done in your theme with the THEME_preprocess_node() function, for placed inside your template.php file, or inside a custom module using HOOK_preprocess_node() function placed inside a custom module.
/**
* Implements THEME_preprocess_node().
*/
function YOURTHEME_preprocess_node(&$vars) {
if ($vars['node']->type == 'article') {
// Remove Add comment link from teaser.
unset($vars['content']['links']['comment']['#links']['comment-add']);
// Remove login/register to comment link.
unset($vars['content']['links']['comment']['#links']['comment_forbidden']);
// Remove comment count for nodes with comments.
unset($vars['content']['links']['comment']['#links']['comment-comments']);
}
}
Note the above code is untested... I may not have the arrays of doom structured correctly there, but you should be able to figure out the right path to the variable to unset using print_r($vars['content'])
If you don't have access to your theme, the Hide Node Links contributed module may work, depending on your needs. It appears that the module disables all node links, not just the "Add Comment" link, and it does it for all view modes, not just the Teaser.