Using get_the_excerpt in edit-post

I think (and assuming) you use (without code, it’s hard to know, how you proceed) add_meta_boxes() to do your job. Then your code is logically standing in custom functions.

Your function to render the metabox, don’t get the $post global, if you didn’t define it, the function need to know from which post it must retrieve the excerpt, so you need to add global $post; this should work

function get_excerpt_custom_metabox(){
    global $post;

    echo get_the_excerpt();
}

The way you want to use the_excerpt filter is not the right way. You must do it like this

add_filter('the_excerpt', 'your_excerpt_function', 10, 2);

function your_excerpt_function($excerpt, $post_id){
    // do what you want,

    return $excerpt;
}

Don’t hesitate to update your question with more code, if you think I’m wrong.