Disable CSS for IE 8 and earlier.

Deregister twentytwelve-ie, which is registered (currently) in function.php on line 157.

function dereg_ie_styles_wpse_99631() {
  wp_deregister_style('twentytwelve-ie');
}
add_action( 'wp_enqueue_scripts', 'dereg_ie_styles_wpse_99631', 1000);

That isn’t just IE8 though. It is registered as less than or equal to IE 9.

If you want to remove all of the stylesheets for IE8 or less you are in for a bumpy ride. Conditional stylesheet loading for IE is handled by browser parsed conditional tags– that is, tags read by IE but not by other browsers. The PHP on the server doesn’t have to worry about what browser is reading the page.

To conditionally remove the primary stylesheet you are limited in options.

The first is user agent sniffing, and it isn’t very reliable. You’d read $_SERVER['HTTP_USER_AGENT'] like wp_is_mobile does, check for IE User Agent strings and then conditionally remove the stylesheet with wp_deregister_script.

function dereg_ie_styles_wpse_99631() {
  wp_deregister_style('twentytwelve-ie');
  if ( strpos($_SERVER['HTTP_USER_AGENT'], 'MSIE') ) {
    wp_deregister_script('twentytwelve-style');
  }
}
add_action( 'wp_enqueue_scripts', 'dereg_ie_styles_wpse_99631', 1000);

That is completely untested and, I think, ill-advised but there you are.

You might be able to cook something up with Javascript but I haven’t even tried that. Javascript can probably do a better job at identifying IE but the rendering time delay would probably be noticeable.