Comments offset

<?php 
global $wp_query, $post; 
$comments_arr = $wp_query->comments; 
$comments_arr = sort( $comments_arr); 
$comments_arr = array_pop( $comments_arr );
$comments_arr = usort($comment_arr, 'comment_comparator');

$comment_count = get_comment_count($post->ID);

 ?>
<h3 id="comments-title"><?php
    printf(
    _n( 'One Response to %2$s', '%1$s Responses to %2$s', get_comments_number(), 'YOUR_THEMES_TEXTDOMAIN' ),
    number_format_i18n( get_comments_number() ),
    '<em>' . get_the_title() . '</em>' 
);
?></h3>
if ( have_comments() ) : 
?><ul class="commentlist"><?php
for ( $i = 0; $i < $comment_count; $i++ )
{
    // do stuff: 
        // This shows you everything you got inside the comments array
        // Call it like this: echo $comments_arr[$i]['comment_author'];
        var_dump( $comments_arr[$i] ); 
    // end do stuff
} // endforeach;
?></ul><?php

elseif ('open' == $post->comment_status) :
    // If there are no comments, but status = open
    ?><p class="nocomments"><?php _e( 'No Comments.', 'YOUR_THEMES_TEXTDOMAIN' ); ?></p><?php
endif; // If $i > 1

else : // or, if comments are not allowed:
    if ( ! comments_open() ) : 
    ?>
        <p class="nocomments"><?php _e( 'Comments are closed.', 'YOUR_THEMES_TEXTDOMAIN' ); ?></p>
    <?php 
    endif; // end ! comments_open() 
endif; // end have_comments() 
?>

Ad your current loop:

No need for $counter = 2; (called nowhere).

If you already got your $comments_arr, why not simply:

$comments_arr = sort( $comments_arr); 
$comments_arr = array_pop( $comments_arr ); 
$comments_arr = usort( $comments_arr );

OR

$comments_arr = unset( $comments_arr[0] ); 
$comments_arr = usort( $comments_arr );