How much time does Google disavow tool has taken to remove the bad links of any website.We have submitted our bad links to this tool but still didn’t get any success in ranking.
You can get more information about the time from Google webmaster tool.
In my view, takes 1-2 weeks.
Or it may take even 1-2 months. Depends on site’s complexity.
I recently found a good article about how to use Google’s disavow links tool the right way. Some may find it useful 
Firstly Google analysis that is the back link really low quality or not and than it do some action. It take almost 10-15 Days.