How to output nothing instead of default avatar?

You can use the get_avatar filter to change the output or avatar_defaults to add new image that can be placed on your server.

Here is an example code for adding new avatar that you can set as default from the Settings > Discussion page.

add_filter( 'avatar_defaults', 'add_new_gravatar_image' );
function add_new_gravatar_image($avatar_defaults) {
    $myavatar="http://yoursite.com/image.png";
    $avatar_defaults[$myavatar] = "Default Gravatar";

    return $avatar_defaults;
}

And if you want to change the output, you have an example on the documentation page for get_avatar.