If you redirect a page to another page, then Google will no longer index the redirected page. Implementing a redirect removes the content.
If you are moving a site from one domain to another without changing the content, you can use the change of address feature in Google Webmaster Tools. When doing so, your new site will take the place of your old site in the Google search results.
Even when your new site has different content, but similar keywords, it may end up ranking well for some of the things that the old site ranked for. A redirect from one site to the other will allow search engines to attribute reputation from the old site to the new site. I'd recommend using 301 redirects rather than 302 redirects because Google is much more likely to pass authority when the redirect is permanent.
If you are removing content completely and not replacing it with something similar, then you will stop ranking for those keywords. The only way to preserve rankings is to leave the old content up and still show it to users.