You can change your code to this:
<?php
$shortcode = do_shortcode('[mingleforum]');
echo apply_filters('my_new_filter',$shortcode);
?>
and then you can interact with that filter
add_filter('my_new_filter','my_new_filter_callback');
function my_new_filter_callback($shortcode){
//to stuff here
return $shortcode;
}