Should a young man leave his fiancée, whom he intends to marry in 4 years, knowing that continuing the relationship now is forbidden (haram), and fearing God's punishment if he leaves her, for breaking her heart?

You must sever the relationship with the girl. It is not permissible to continue it under the pretext of fearing to hurt her feelings; in fact, you will be sinful if you remain in contact with her in this manner. Since you are currently unable to marry, occupy yourself with what benefits you in your religion and worldly life until you are able to marry. If you can propose to her now, on the condition that she waits for you until you are able to afford the marriage expenses, then there is no objection. However, it is not permissible for there to be any relationship between you involving meetings or communications until you conclude the legal marriage contract with her. And whoever gives up something for the sake of Allah, Allah will compensate him with something better.