WP_Query to display posts by category in Wordpress (in custom post types)

Here is how you do it. You needed a foreach loop to cycle through the categories.

<?php
$cats = get_categories();

foreach ($cats as $cat) {
$args = array(
'post_type' => 'support',
'tax_query' => array(
    array(
        'taxonomy' => 'category',
        'field'    => 'term_id',
        'terms'    => $cat->cat_ID,
        ),
    ),
);
$query = new WP_Query($args);

if ( $query->have_posts() ): ?>
    <p><?php echo $cat->cat_name ; ?></p> <?

   while($query -> have_posts()) : $query -> the_post(); ?>
      <h2><a href="<?php the_permalink(); ?>"><?php the_title(); ?></a></h2>
      <p><?php the_content(); ?></p> <?php
   endwhile;
endif; 

// Added this now 
wp_reset_query() ; 
}