There are a lot of useful tools for finding and fixing broken links. But I use Google Analytics and Ahrefs, they are helpful for easily finding broken links.
I know also that a lot of people use Hexometer tool, it also has Chrome extension and Firefox addon.
So after finding broken links, there are a number of ways of disabling them. For example,find the contact details of the website owner and ask him to remove the link. Get rid of the domain and start all over.
One more useful tool is LinkResearchTools (LRT),it provides excellent value for money when it comes to cleaning up your bad backlinks.