If you think they are cluttering the home page, you have a couple of options.
If they really are very bad, flag them for deletion. We don't like to delete questions outright for a few reasons I'll get to later, but if it's already closed and heavily downvoted sometimes we'll short circuit the automatic and community processes that area already in place.
If you just want them gone from the home page, pile on a downvote. At -4 questions stop appearing on the home page.
The reasons that we don't delete these outright are the following:
There are community processes that we'd prefer to take place. The first is that high rep users can delete these themselves, this is relatively rare, but we'd rather they take the lead here. But more importantly, there are chances for some of these questions to get redeemed and for the users to learn how to ask better questions either from fixing the post themselves, someone coming and helping them fix it, or simply by having a comment discussion that points them to a better future. We don't want to short circuit this.
There are automatic processes in place that make this a non-issue. Namely that relatively old (30ish days?), downvoted questions without upvoted answers and that haven't been edited recently are deleted automagically.
We also don't want to delete potentially useful content. Even if the question is closed and downvoted to oblivion, sometimes an answer will be really good and in those cases its worth keeping the question around just so the answer still exists in a visible place on the Internet.
So no, we won't be scrubbing all the downvoted questions on the home page. You're welcome to downvote them (you did that before posting this, right?), and flag them if you must, but be mindful of the fact that we're not in a hurry to delete them so you may find your flags declined.
Oh, and don't worry too much about the home page, you're seeing the logged in version. most people who visit the site (if they ever get to the home page), will see a prettier, more representative group of questions (spin up an anonymous session to see what I'm talking about).