How Can I limit the visible part of the short-description on the Category page?

Normally if you set a custom excerpt it shows the full text of that excerpt. In this case the length is being limited by the PHP function mb_substr to a limit of 180 characters or whatever the shop_dec_len option is set to. This tells me that you can either modify that parameter of mb_substr directly or there is an option somewhere in the admin and you don’t even need to change the code. To modify it directly you could do the following:

<?php if ($post->post_excerpt && $post->post_excerpt != "") echo '<div     itemprop="description" class="desc">' . mb_substr ( strip_tags($post->post_excerpt), 0, 100 ) . $len . '</div>'; ?>

For a different way to trim the excerpt, you might look into [trim_word()][2] which is a neat function someone wrote for trimming without breaking words:

/**
 * trims text to a space then adds ellipses if desired
 * @param string $input text to trim
 * @param int $length in characters to trim to
 * @param bool $ellipses if ellipses (...) are to be added
 * @param bool $strip_html if html tags are to be stripped
 * @return string 
 */
function trim_text($input, $length, $ellipses = true, $strip_html = true) {
    //strip tags, if desired
    if ($strip_html) {
        $input = strip_tags($input);
    }

    //no need to trim, already shorter than trim length
    if (strlen($input) <= $length) {
        return $input;
    }

    //find last space within length
    $last_space = strrpos(substr($input, 0, $length), ' ');
    $trimmed_text = substr($input, 0, $last_space);

    //add ellipses (...)
    if ($ellipses) {
        $trimmed_text .= '...';
    }

    return $trimmed_text;
}

So that might look like:

<?php if ($post->post_excerpt && $post->post_excerpt != "") echo '<div     itemprop="description" class="desc">' . trim_words( $post->post_excerpt, 100, false, true ) . $len . '</div>'; ?>