Redesigning is an undertaking on a site from an SEO perspective, and should be well thought of well before you implement it.
You should not re add the website to WMT, or remove URLs. If you aren't using a CMS that dynamically generates sitemaps, I would submit the sitemap once the site is live and delete the old one. There is no real need to ask the googlebot to recrawl your site, i'm assuming you have links to your site, and it is added in WMT, so google already knows the site is there (especially if you have indexed URLs)
As far as deleting old pages, and creating new ones, this will require a lot of thought and effort on your end. What I would do, is look at all the URLs on your website currently, then determine what ones are going to be removed, and what ones will simply have the same content and the URLs changed. The ones that have the URLs changed, I would just redirect to the new URL. The pages that are being removed completely, i'd ask myself, what will the next-most relevant page on the new site be to this page? I would then have the redirect go to that URL.
The other case of this is "category" and "sub-pages" of that category. If you decide to remove all the sub pages to and just have a single category page, redirect all the sub pages for a category page. For example, if you were selling a printer, and originally had a separate page for each feature of the printer (scanning, fax, ink efficiency etc..) and now are showing the features on a /printer/features/ page I would Simpy redirect the /features/fax/ page to the /printer/features. Again, for redirects it's just doing the next-most relevant URL.
Also, once the new site is live, it wouldn't hurt to contact your top links on pages that you redirected and ask them to change the URL of the link, stating that you redesigned the site and the URL have changed. Remember with 301s you lose 1-10% of the link juice that is passed through, so for high-quality links, this could be the difference in top rankings.
I can't emphasize enough the importance of implementing all the redirects necessary, I've had times where I literally had WMT warnings for 9,000 found URLs because a client didn't plan properly and didn't implement the 301s. An increase in 404s can affect your rankings.
Hope this helps
Zach