I want to implement JetPack comments plugin on my external WordPress site. I assume it stores the comments in the local database of the website also. Is it possible to disable that option so that it does not store comments in local database?
The Jetpack comment feature is only used to manage the input process. It displays a form element as an iframe from wordpress.com and sends the comments back to your blog. Your comments are stored locally and not in the cloud.
Therefore it is not possible to disable the storage of the comments in your database because otherwise they wouldn't be stored at all.
You could use the following services to store your comments in the cloud. But I would still advise to always use the feature to backup your comments in the local database.