Yes. You can use the save_post action and do it here is some function that remove the default wordpress category if there is some other category selected.
I added some comments so you will understand the process.
function remove_uncategorized($post_id) {
// get default category
$default_category = (int)get_option('default_category');
// check if the post is in the default category
if(in_category($default_category, $post_id)) {
// get list of all the post categories
$post_categories = get_the_category($post_id);
// count the total of the categories
$total_categories = count($post_categories);
// check if the post is in more than 1 category (the default one and more..)
if($total_categories > 1) {
// remove the default category from the post
wp_remove_object_terms($post_id, $default_category, 'category');
}
}
}
add_action( 'save_post', 'remove_uncategorized' );