Similar to exporting pages, is there any way we can export blocks data?
You can export blocks via API, but there's no UI for that (like the one for pages).
Check this post: http://world.episerver.com/forum/developer-forum/Episerver-7-CMS/Thread-Container/2013/6/How-to-exportimport-unused-shared-blocks-and-folders-from-global-library/
You can do an export by putting the blocks you want to export into a ContentArea on page, and export that page.. Make sure that you export references content too.
It's not working 100% but hope it helps you enough.