You can inject \Magento\Framework\App\CacheInterface\Magento\Framework\App\CacheInterface
as dependency and assign it to ($__cacheManager)$_cacheManager
in your constructor or get it from de $context$context
(if you have) and then after save changes clean the related cache that way:
$this->_cacheManager->clean(array(tags[tag1,tag2..tagN]));
youYou could find a complete implementation in Catalog\Product\Model
I guess you could use the "get" method of the ObjectManager to get the cache instance too, but I'm not sure if is a good practice.