How to show parents of current page category, excluding the category?

The easiest way to do this, is by retrieving the direct parent of the current page category and then use get_category_parents on that category. Like this:

// supposing $cat contains the category ID
// load category object
$cat_obj = get_category ($cat);
// retrieve parent ID from object;
$parent = $cat_obj->parent;
// retrieve list of parent categories without current category
echo get_category_parents ($parent, true, ' » ');

(Untested but should work)