The topic isn't new, we actually covered it a couple months ago under the title Want To Disavow Links In Google Now? 404 The Target Page. But I write so much here that I am sure many of you missed it. Since John Mueller at Google said it again in a new Google Webmaster Help thread, I thought I'd cover the topic again.
When you have tried and tried and tried to get bad links pointing to your site removed and have failed and failed time and time again, then as a last resort, if you can, you should 404 the page with the bad links pointing towards it. Now this is not always possible, sometimes the bad links are pointed to your home page, but when not and when it is pointed to a specific section or specific web page(s) of your site, just 404 the page and eventually, Google will stop counting those links (good and bad) towards that page.
In particular, if links to a specific page are causing a problem for your site (regardless of how), then removing those links is generally the best solution. If you absolutely can't remove those problematic links and if you're certain that the page itself is otherwise not that relevant for the rest of your site, then removing the page that's being linked to (returning 404/410) will also help us to drop the links to that page. Obviously, this is not a perfect situation (you wouldn't want to remove an important page unless it's really necessary), so I'd recommend really taking steps to make sure that this is really the source of the problem.
Again, this is very similar to what he said back a few months ago.
Extreme circumstances require extreme measures?
Forum discussion at Google Webmaster Help.