Filter custom taxonomy posts via AJAX

I don’t know why you would see WP_Query arguments in the data returned, a copy/paste of your code here (with a few adjustments- post type, taxonomy, and term name) does not produce that result.

Getting the post excerpt via get_post_field will only work if you explicitly entered an excerpt in that field, it will not generate one from post_content. You’ve also not defined $post_id, but that shouldn’t matter as it will fall back to the current $post.

Here’s a version with the unnecessary bits removed, and some slight adjustments:

function my_ajax_pagination() {
    $name = $_POST['termname']; 
    $args = array(
        'post_type' => 'myposttype',
        'posts_per_page' => -1,
        'tax_query' => array(
            array(
                'taxonomy' => 'mytaxonomyname',
                'field' => 'slug', 
                'terms' =>  $name 
            )
        )
    );
    $posts = new WP_Query( $args );

    if( ! $posts->have_posts() ) { 
        echo "I don't work yet";
    }
    else {
        while ( $posts->have_posts() ) { 
            $posts->the_post();
            echo get_the_excerpt();
        }
    }

    die();
}

One other change I would suggest is to put your post data into an array and return it via wp_send_json rather than echo data and markup directly.