Get the excerpt for a post created by the related author

your code is not wrong. However, in my opinion, it would be better to handle the task in a slightly different way.

Usage

In your functions.php:

/* This function returns the related posts in an array of objects. You can set how many items you want retrieve.If not set, the number of items will be set to "1". */
function get_related_author_posts( $items = 1 ) {
  global $authordata, $post;
  $authors_posts = get_posts( 
  array( 
      'author' => $authordata->ID, 
      'post__not_in' => array( $post->ID ), 
      'posts_per_page' => $items, 
      'post_type' => 'artistblog' 
    ) 
  );
  return $authors_posts;
}

In your template file:

<?php 
  $related_posts = get_related_author_posts( 3 );
  foreach( $related_posts as $post ) : setup_postdata( $post ); ?>
  <div class="artist-blog-thumb">
    <a href="https://wordpress.stackexchange.com/questions/111225/<?php the_permalink(); ?>"><?php the_post_thumbnail( 'medium' ); ?></a>
  </div>
  <h3><a href="https://wordpress.stackexchange.com/questions/111225/<?php the_permalink(); ?>"><?php the_title(); ?></a></h3>
  <div class="excerpt">
    <p><?php the_excerpt(); ?></p>
  </div>
<?php endforeach; wp_reset_postdata(); ?>

Let me know if you get stuck.