You can simply loop over the categories that you don’t need. get_the_category()
return an array of categories that the post belongs to.
With that in mind, you can do the following: (Just remember to change 21
and 41
to your desired ID’s)
$categories = get_the_category();
foreach ( $categories as $category ) {
if( 21 === $category->cat_ID || 41 === $category->cat_ID ) {
continue;
}else{
echo $category->cat_ID . '</br>';
}
}