How to remove a stylesheet provided by a contrib module?
I think using hook_css_alter() in a custom module/theme would be the easiest solution:

function MYMODULE_css_alter(&amp;$css) {
  // Get the path to the module
  $path = drupal_get_path('module', 'field_group');

  // Remove the unneeded files from the css array
  unset($css[$path . '/field_group.css']);
  unset($css[$path . '/field_group.field_ui.css']);
}


There are also other CSS files in the Field Group module:


horizontal-tabs/horizontal-tabs.css
multipage/multipage.css


In case you're look to remove absolutely all the CSS that Field Group introduces.