This is not a common expression. In fact this is probably the only time you will ever see that phrase. It is a very creative use of words.
Heartbreak is when someone is really sad, and they are so sad it feels like their heart will break. In this case heartbreak is the sadness experienced after a relationship has ended.
A taboo is something which society believes is unacceptable. It is something that a person should not do, otherwise other people will not be happy with them.
So this very unusual set of words "heartbreak 的 taboo" implies that getting really sad and upset for a long time after a relationship breakup is something that society doesn't accept... society says that people should just "get over it" and move on.
So this person wants to "remove the taboo of heartbreak", so that heartbreak is viewed as normal and natural, so that if someone does not "get over it", that's ok.