Wordpress - List all posts in custom post type by taxonomy

Try this

$custom_terms = get_terms('custom_taxonomy');

foreach($custom_terms as $custom_term) {
    wp_reset_query();
    $args = array('post_type' => 'custom_post_type',
        'tax_query' => array(
            array(
                'taxonomy' => 'custom_taxonomy',
                'field' => 'slug',
                'terms' => $custom_term->slug,
            ),
        ),
     );

     $loop = new WP_Query($args);
     if($loop->have_posts()) {
        echo '<h2>'.$custom_term->name.'</h2>';

        while($loop->have_posts()) : $loop->the_post();
            echo '<a href="'.get_permalink().'">'.get_the_title().'</a><br>';
        endwhile;
     }
}

We get all the terms of a taxonomy, loop through them, and fire off a title link to each post that belongs to that term. If you need to reorder the taxonomy terms, you can do so with a plugin pretty easily. Reorder Taxonomy, I believe. But pay attention that this plugin adds(!) another column to your table on activation and does not remove it upon deactivation!

Not a particularly elegant solution but you can create multiple queries each for the specific terms and then output them. Hopefully someone can come up with a nicer way of automatically pulling the terms to modify the output/sorting. But this would get you going.

<?php

//First Query for Posts matching term1
$args = array(
    'tax_query' => array(
        array(
            'taxonomy' => 'taxonomy_1',
            'field' => 'slug',
            'terms' => array( 'term1' )
        ),
    ),
    'post_type' => 'my-post-type'
);
$query = new WP_Query( $args );

if ( have_posts() ) {

    $term = $query->queried_object;

    echo 'All posts found in ' . $term->name;

    while ( have_posts() ) : the_post();
        //Output what you want
        the_title();
        the_content();
    endwhile;
}

//RESET YOUR QUERY VARS
wp_reset_query();

//Second Query for term2
$args = array(
    'tax_query' => array(
        array(
            'taxonomy' => 'taxonomy_1',
            'field' => 'slug',
            'terms' => array( 'term2' )
        ),
    ),
    'post_type' => 'my-post-type'
);
$query = new WP_Query( $args );

if ( have_posts() ) {

    $term = $query->queried_object;

    echo 'All posts found in ' . $term->name;

    while ( have_posts() ) : the_post();
        //Output what you want
        the_title();
        the_content();
    endwhile;
}