How to create dependent field in Customizer?

You can get and check the value of your theme mod as you normally do anywhere.

This code is tested and working (the code inside cyb_customizer() is exactly the code you posted in the question, only added add_section part):

function flag_is_custom_excerpt_enabled(){
    $blueplanet_options = get_theme_mod( 'blueplanet_options');
    if( empty( $blueplanet_options['theme_enable_custom_excerpt'] ) ) {
        return false;
    }
    return true;
}

add_action( 'customize_register', 'cyb_customizer' );
function cyb_customizer( $wp_customize ) {


    $wp_customize->add_section(
        'admin_section',
        array(
            'title' => 'Admin section',
            'description' => 'Admin section',
            'priority' => 0,            
        )
    );

    $wp_customize->add_setting( 'blueplanet_options[theme_enable_custom_excerpt]',
        array(
            'default'    => false,
            'capability' => 'edit_theme_options',
         )
      );
      $wp_customize->add_control(
          'theme_enable_custom_excerpt',
          array(
            'label'       => 'Enable Custom Excerpt Length',
            'section'     => 'admin_section',
            'settings'    => 'blueplanet_options[theme_enable_custom_excerpt]',
            'type'        => 'checkbox',
          )
       );
      $wp_customize->add_setting( 'blueplanet_options[theme_custom_excerpt_length]',
         array(
            'default'              => 20,
            'capability'           => 'edit_theme_options',
         )
      );
      $wp_customize->add_control(
          'theme_custom_excerpt_length',
          array(
            'label'           => 'Custom Excerpt Length',
            'section'         => 'admin_section',
            'settings'        => 'blueplanet_options[theme_custom_excerpt_length]',
            'type'            => 'text',
            'active_callback' => 'flag_is_custom_excerpt_enabled',
          )
        );

    }