According to Catholicism, is marrying a divorced woman a sin of continual adultery? In the Sermon on the Mount, Jesus says that marrying a divorced woman is a sin. Certainly having sex with a married woman is adultery, but Jesus also calls it adultery to marry a divorced woman.

However he says this in the context of the Sermon on the Mount. “You have heard it said X, but I say to you Y” where Y seems to really redefine terms to be much more expansive and broad.

No one is really going around gouging their eyes out to prevent looking at married women lustfully.  And Jesus says “if your eye offends you” which implies the sin of adultery already took place. However, it ony took place in the heart.

Same with being angry with your brother. The sin of murder has taken only place in the heart.

But when it comes to divorce, Jesus seems to describe real adultery. It doesn’t make much sense to me when he is quoted as saying that te man commits adultery if he marries another woman. Adultery was ONLY defined as a man sleeping with a married WOMAN, in fact Jewish men had polygamy, and in fact it was commanded to marry your deceased brother’s wife even if you already were married, an example brought to Jesus by the Sadduccees.

So, according to Catholicism, how does the definition of adultery and the context of the Sermon on the Mount affect what we should do? No one is plucking their eyes out or cutting off their hands, so was it just meant to shock people? Mentioning adultery, I mean.
Yes it is a sin, provided the divorced person was truly married.

What is meant by “truly married”, you say?

In short it is when two people get married AND the outward appearances
of marriage do indeed reflect the inner convictions of both.  If this is not the case, it is possible to get what is called an annulment, which can be considered a divorce but properly speaking if the marriage was truly a marriage then it would be impossible to separate the two persons. Rather an annulment is about recognizing that the marriage wasn't really a marriage in the first place.  

The long version is presented here in the Code of Canon Law: 


  CHAPTER IV.
  
  MATRIMONIAL CONSENT
  
  Can.  1095 The following are incapable of contracting marriage:
  
  1/ those who lack the sufficient use of reason;
  
  2/ those who suVer from a grave defect of discretion of judgment
  concerning the essential matrimonial rights and duties mutually to be
  handed over and accepted;
  
  3/ those who are not able to assume the essential obligations of
  marriage for causes of a psychic nature.
  
  Can.  1096 §1. For matrimonial consent to exist, the contracting
  parties must be at least not ignorant that marriage is a permanent
  partnership between a man and a woman ordered to the procreation of
  offspring by means of some sexual cooperation.
  
  §2. This ignorance is not presumed after puberty.
  
  Can.  1097 §1. Error concerning the person renders a marriage invalid.
  
  §2. Error concerning a quality of the person does not render a
  marriage invalid even if it is the cause for the contract, unless this
  quality is directly and principally intended.
  
  Can.  1098 A person contracts invalidly who enters into a marriage
  deceived by malice, perpetrated to obtain consent, concerning some
  quality of the other partner which by its very nature can gravely
  disturb the partnership of conjugal life.
  
  Can.  1099 Error concerning the unity or indissolubility or
  sacramental dignity of marriage does not vitiate matrimonial consent
  provided that it does not determine the will.
  
  Can.  1100 The knowledge or opinion of the nullity of a marriage does
  not necessarily exclude matrimonial consent.
  
  Can.  1101 §1. The internal consent of the mind is presumed to conform
  to the words and signs used in celebrating the marriage.
  
  §2. If, however, either or both of the parties by a positive act of
  the will exclude marriage itself, some essential element of marriage,
  or some essential property of marriage, the party contracts invalidly.
  
  Can.  1102 §1. A marriage subject to a condition about the future
  cannot be contracted validly.
  
  §2. A marriage entered into subject to a condition about the past or
  the present is valid or not insofar as that which is subject to the
  condition exists or not.
  
  §3. The condition mentioned in §2, however, cannot be placed licitly
  without the written permission of the local ordinary.
  
  Can.  1103 A marriage is invalid if entered into because of force or
  grave fear from without, even if unintentionally inflicted, so that a
  person is compelled to choose marriage in order to be free from it.
  
  Can.  1104 §1. To contract a marriage validly the contracting parties
  must be present together, either in person or by proxy.
  
  §2. Those being married are to express matrimonial consent in words
  or, if they cannot speak, through equivalent signs.