Matthew 5:31–32 (NKJV)
31 “Furthermore it has been said, ‘Whoever divorces his wife, let him give her a certificate of divorce.’ 32 But I say to you that whoever divorces his wife for any reason except sexual immorality causes her to commit adultery; and whoever marries a woman who is divorced commits adultery.
Matthew 19:8–9 (NKJV)
8 He said to them, “Moses, because of the hardness of your hearts, permitted you to divorce your wives, but from the beginning it was not so. 9 And I say to you, whoever divorces his wife, except for sexual immorality, and marries another, commits adultery; and whoever marries her who is divorced commits adultery.”
So they can separate, but not remarry or engage in relations with others because that would be adultery. Just like St. John the Baptist reproving Herod for his marriage.