Remove “Continue Reading” Link From the Teaser Excerpt Only

Change standard text for all excerpts:

function custom_excerpt_more($more) {
   global $post;
   $more_text="...";
   return '… <a href="'. get_permalink($post->ID) . '">' . $more_text . '</a>';
}
add_filter('excerpt_more', 'custom_excerpt_more');

Create your own excerpt function:

// Rafael Marques Excerpt Function ;)
function rm_excerpt($limit = null, $separator = null) {

    // Set standard words limit
    if (is_null($limit)){
        $excerpt = explode(' ', get_the_excerpt(), '15');
    } else {
        $excerpt = explode(' ', get_the_excerpt(), $limit);
    }

    // Set standard separator
    if (is_null($separator)){
        $separator="...";
    }

    // Excerpt Generator
    if (count($excerpt)>=$limit) {
        array_pop($excerpt);
        $excerpt = implode(" ",$excerpt).$separator;
    } else {
        $excerpt = implode(" ",$excerpt);
    }   
    $excerpt = preg_replace('`\[[^\]]*\]`','',$excerpt);
    echo $excerpt;
}

Use <?php rm_excerpt(); ?> when you want display custom excerpt. First value set words limit and second value set separator. Example: <?php rm_excerpt(10,' (...)'); ?>. To create separate link “read more”, insert <a href="https://wordpress.stackexchange.com/questions/83160/<?php the_permalink(); ?>" title="<?php the_title(); ?>">Read More?</a>

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