Filter posts by categories ajax is showing all the posts

In your code, I have found 2 issues:

1) In your ajax function ajax_filter_get_posts(), you have missed tax_query in your arg.

Your ajax function ajax_filter_get_posts() should be as below:

function ajax_filter_get_posts( $taxonomy ) {

 // Verify nonce
 if( !isset( $_POST['afp_nonce'] ) || !wp_verify_nonce( $_POST['afp_nonce'], 'afp_nonce' ) )
   die('Permission denied');

 $taxonomy = $_POST['taxonomy'];

 // WP Query
   $args = array(
   'exclude' => '1,2,4,5,7,8,9,10,11,12',
   'post_type' => 'post',
   'nopaging' => true, // show all posts in one go
   );
 echo $taxonomy;
 // If taxonomy is not set, remove key from array and get all posts
 if( !$taxonomy ) {
   unset( $args['tag'] );
 }else{
   // This is the code which you are missing. You need to add taxonomy query if taxonomy is set.
   $arg['tax_query']= array(
     array(
       'taxonomy' => 'category',
       'field' => 'slug',
       'terms' => array( $taxonomy ),
       'include_children' => true, // set true if you want post of its child category also
       'operator' => 'IN'
           ),
   );
 }

 $query = new WP_Query( $args );

 if ( $query->have_posts() ) : while ( $query->have_posts() ) : $query->the_post(); ?>
     <div class="col-md-4">
       <div class="img-thumb">
           <a href="https://wordpress.stackexchange.com/questions/260141/<?php the_field("link_do_case'); ?>">
               <?php the_post_thumbnail(); ?>      
           </a>                                                                    
       </div>
       <small><?php the_title(); ?></small>
   </div>

 <?php endwhile; ?>
 <?php else: ?>
   <h2>Case não encontrado</h2>
 <?php endif;

 die();
}

2) In your structure page, replace the tag line link with below line:

echo '<option value="' . $term_link . '" class="tax-filter" title="'.$term->slug.'">' . $term->name . '</option> ';

3) In your jQuery, change the way you are getting selected taxonomy value:

var selecetd_taxonomy = jQuery(this).find('option:selected').attr("title");

By doing above 3 changes you will get post of only selected category.

Hope this will help you.