The Disavow Tool simply takes too long to work.
You can do a search for old threads on this topic on this forum.
This seems to be the consensus.
The key is to create more content, do more interlinking, and try to offset the negative backlinks that somebody is intentionally pointing at your site.
Also, if you are the target of a negative SEO campaign, depending on how they do it, it would be very easy for Google to discount those links.
In fact, some people have posted on this forum that either they or somebody tried to do negative SEO on them, and it didn't really work because the links were built pretty much within a very narrow period of time.
Talk about unnatural!
There's even some chatter along the lines that Google has a built-in "unnatural link activity" filter so this is basically interpreted as noise.
Still, this is speculation so do your research and be proactive in terms of adding more content and interlinking as well as earning higher quality backlinks from the rest of the Internet.