I am always looking for new bands/music, usually genre specific.
Is it possible to download all or part of the database some format?

You typically can't download a website's data directly. There is an unofficial API for MA, but last time I tried it didn't work. Are you looking for an offline version? What's wrong with just using the site?

Advanced Search -> set the genre you want, maybe exclude combinations you don't want ->perform search -> bookmark that.

If you want black metal, but no black/death metal search for "black -death".

You could also copy that generated list by hand into an excel list or word or whatever if you really want it local.