Add below functions to your function.php file in WordPress child theme

add_action('woocommerce_after_shop_loop_item_title', 'sm_description_in_shop_loop_item', 3 );
function sm_description_in_shop_loop_item() {
    global $product;

    // HERE define the number of words
    $limit = 10;

    //$description = $product->get_description(); // Product description
    // or
    $description = $product->get_short_description(); // Product short description

    // Limit the words length
    if (str_word_count($description, 0) > $limit) {
        $words = str_word_count($description, 2);
        $pos = array_keys($words);
        $excerpt = substr($description, 0, $pos[$limit]) . '...';
    } else {
        $excerpt = $description;
    }

    echo '<p class="description">'.$excerpt.'</p>'; 
}