To burn someone off is to dump them, cease involvement with or do something to belittle them. You can either 'burn someone off' or 'get burnt' if they do it to you. The person who gets burnt will often have a feeling of rejection
Mike: "Hey are you still going out with that girl?"
Bill: "Nar, I decided to burn her off"
Henry: "Hey you guys wanna go to that party tonight?"
Dave: "Nar, it wont be any good"
Stu: "Haha, Henry you just got burnt"