She formed a relationship with someone else - should he fulfil his promise to marry her?
Question

I am a young Muslim man and am religiously committed. I fell in love with a girl and promised to marry her, but she formed a relationship with another man. When I found out, she admitted that she was wrong and asked me to forgive her, but I no longer trust her and I do not like the way she behaves. Is it haraam for me to break my promise to her or not, although she is in the wrong? What do you advise me to do?.
Praise be to Allah.Firstly:
What we advise you to do is to let her go. Breaking your promise to marry her is justified according to sharee’ah. The Messenger (peace and blessings of Allaah be upon him) encouraged us to choose a wife who is religiously committed, so look for such a one, and forget about this one, and Allaah will give you one that is better than her. 
Secondly: 
You should note that for a man and woman to form a relationship and agree to marry, with the conversations and meetings that that involves, is something haraam. This has been explained in the answers to many questions on this site, such as questions no. 20949 and 1114. 
If you have done any such thing, then you must hasten to repent from this sin and resolve not to do it again. 
You describe yourself as religiously-committed, so you must adhere to the rulings of Islam and avoid that which Allaah and His Messenger have forbidden. May Allaah help you to the best of words and deeds. 
And Allaah knows best.