I have made some changes in my website meta tags and title. But in Search result the old title and description is showing in SERP. What I should do to remove old cached rich snippet for my site.
Old snippet cache will be automatically replaced with the new one when Google crawl your page next time. Normally it take maximum 5 days, rest of the things depend upon your site status.
This is true in most instances for the cached snapshot only, not the META information that the OP was talking about. There is nothing you can do except wait, Google updates when they want to. By the time you'd get ahold of anyone at google about this, it would likely appear for you. Do you have a free Google Webmaster Tools account? Id imagine that helps.