Permanently deleting old pages so Google doesn't index them?

Hi,

New to Zen Cart and am trying to get client's SEO and XML sitemap together. I've noticed that Google is still seeing and indexing hundreds of product pages that the client has supposedly deleted and is no longer visible on the site. I have no idea why it's still being seen even though I just regenerated their site map today and why it's still being indexed.

I'm thinking maybe there's a clear cache function or something but I'm not seeing it.

Any advice would be greatly appreciated.

Google doesn't immediately re-index your site on-demand. They do it when they choose to do it. And they don't always pick up your submitted site-map immediately either.

The correct approach is to make sure that anyone (including google) gets a proper 404-not-found response when they hit those "old" pages.
Your hosting company can help you sort out whatever is preventing Google from getting a 404 correctly (ie: perhaps you have some weird rewrite rules going on that send visitors to some other place instead of properly giving a 404-not-found.).

As far as Zen Cart goes, if you were talking about old "pages" within Zen Cart (such as non-existent products, or Zen Cart content pages etc that you've removed), then Zen Cart would send a proper 404 response.
But you seem to be talking about pages from the site from before Zen Cart was used, so it seems like it's some other issue you need to sort out outside Zen Cart