How to get only cart sidebar Layout block in magento

In your controller you could try something like this:

$block = $this->getLayout()->createBlock('checkout/cart_sidebar');

$block->setTemplate('checkout/cart/sidebar.phtml');

Depending on your configuration (Config -> Checkout -> Shopping Cart Sidebar),

you can render the template with  

$block->toHtml(); 

If you use a custom template, you could ignore the config value so it renders anytime.