Crop image from get_theme_mod Customizer field

With your method it would be very tricky, if it’s possible at all. What you could do is use a custom header with flexible dimensions. That would allow the user to upload the header image and then crop it how ever they needed easily.

// Register Theme Features
function custom_theme_features()  {

// Add theme support for Custom Header
$header_args = array(
    'default-image'          => 'http://example.com/image.png',
    'width'                  => 0,
    'height'                 => 0,
    'flex-width'             => true,
    'flex-height'            => true,
    'random-default'         => false,
    'header-text'            => false,
    'default-text-color'     => '',
    'uploads'                => true,

);
add_theme_support( 'custom-header', $header_args );
}

// Hook into the 'after_setup_theme' action
add_action( 'after_setup_theme', 'custom_theme_features' );