adding a filter to a shortcode?

<?php echo do_shortcode('[mingleforum]'); ?>

inserts the mingle forum into my content!

is it possible to use add_filter() on that?

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;
}