"신경 쓰지마" means, "Never mind" or "None of your business". It can be used in both positive and negative situation. For instance, if one of your friends, who is not close with you, she or he is interfering or bothering you, you could say, "신경 쓰지마" or "신경 꺼". It doesn't sound nice..even a little bit of rude even if they're not close with you. So we generally use "신경 쓰지마" in a positive meaning as "Never mind" or "Don't Worry" with "걱정하지마". In other words you don't want to let someone worry about doing something.
Meanshile "걱정 하지마" means, literally "Don't worry", and also "Never mind". It doesn't have a negative nuance.
^^