We regularly expire pages at which time we start sending back a 410 status code. Is there a way that we can inform Google as soon as possible which pages to remove from its index?

I know that Google Webmaster Tools has a URL removal tool, but is there a mass URL removal tool available anywhere?

Yes, In Google Webmaster tools is a way to remoce the useless pages.I tried it many times, You can also try this and solves your problem.

Right but it only allows you to manually remove one page at a time. I'm looking for an automated way of removing multiple pages (i.e. in sitemap format, etc)