I want to stop google bot from accessing my <blockquote> tag because blockquote mostly contain duplicate content. is it possible to do so?
Nope. As for duplicate content, if the blockquote element is being used properly, there won't be enough duplicate content on your page to reduce the weight of the text (or the keywords in them) anyway.
Yes, you could put the blockquote element within these tags to stop it indexing your code; <!--googleoff: index--> your code <!--googleon: index--> However, I'm sure it's bordering on pointless unless you have a lot of content there.
You did say googlebot. The other way is a simple PHP script to stop the content block loading when a search engine useragent accesses your site.