How to remove class attributes from custom menu markup?

You can use the nav_menu_css_class filter to remove the classes that you want from your menu-item.

See the example below, to remove ALL the CSS classes that are appended to you menu items:

add_filter('nav_menu_css_class','remove_nav_menu_classes');
function remove_nav_menu_classes($classes) {
    return array(); 
}

Do a print_r($classes) if you want to know which classes are active in your menu.