Why excerpt is Displaying same in Random Posts list

You are trying to use the_title() and the_excerpt() functions outside the wordpress loop, therefore, they will not work.

I suggest you try something like :

$args = array( 'posts_per_page' => 12, 'orderby' => 'rand', 'post_status' => 'publish', 'offset' => 1);
$query = new WP_Query($args);
while($query->have_posts()){
    $query->the_post();
    // the_excerpt() will now work as expected
}