Many new webmasters have used Disavow Tool but never achieved the result they wanted. You have to make sure that you need the best site with good page rank and more over that particular site should have a good reach among the audience.
You have to keep in mind that your original rankings were based off of Google counting those links – now they won’t because
(1) Google caught them and/or
(2) you removed them or disavowed them.
Google has replied to one of its webmaster regarding this issue
In process of removing spam back links, you will lose some sort of weight age of links and trust factor in search engines. You need to improve your authority and build few related high quality back links. to make your website perform better.
Every time you build a backlink you need to check whether the site has good authority or not. Just building links is not enough buid relationship which will be helpful for longer run.