Praise be to Allah.
We put this question to Shaykh Muhammad ibn Saalih al-‘Uthaymeen, may Allaah preserve him, who answered as follows:
He does not have to (cut off ties with his non-Muslim friends), so long as they are not causing him any harm. But he can withdraw from them gradually. He should tell them about Islam, because if they see that he has become Muslim, they may become Muslim too. And Allaah knows best.