Example of Drupal's hook_css_alter and hook_js_alter to remove unwanted core and contrib styles and scripts.

gistfile1.php

/**
 * Implements hook_js_alter().
 *
 * Remove unwanted module JS.
 */
function mytheme_js_alter(&$javascript) {

  $removal_list = array(
    'google_cse' => array(
      '/google_cse.js',
    ),
    'menu_attach_block' => array(
      '/menu_attach_block.js',
    ),
  );

  foreach ($removal_list as $module => $scripts) {
    $module_path = drupal_get_path('module', $module) ;

    foreach ($scripts as $script) {
      $script_path = $module_path . $script;
      if (isset($javascript[$script_path])) {
        unset($javascript[$script_path]);
      }
    }
  }
}

/**
 * Implements hook_css_alter().
 *
 * Remove unwanted module CSS.
 */
function mytheme_css_alter(&$css) {

  $removal_list = array(
    'google_cse' => array(
      '/google_cse.css',
    ),
    'system' => array(
      '/system.theme.css',
      '/system.menus.css',
    ),
  );

  foreach ($removal_list as $module => $stylesheets) {
    $module_path = drupal_get_path('module', $module) ;

    foreach ($stylesheets as $stylesheet) {
      $css_path = $module_path . $stylesheet;
      if (isset($css[$css_path])) {
        unset($css[$css_path]);
      }
    }
  }
}