I want to create a website that will grab content from other news websites using their RSS and insert it in my database. I am only going to show the title and an excerpt with a link to the original post.
Is this a good idea?
No, because you're using someone else's content
Will Google ban my website?
If you keep it up, then Google will eventually notice, especially if the level of copying is very frequent (a.k.a. server slowdown).
Is it bad for SEO?
bad is a light word. It's terrible because a) your content is thin, and b) your content duplicates someone else's. You should look at webmaster quality guidelines from any popular search engine such as Google.
and is it against Google Adsense rules?
Definitely. You need original content.