Did the Lord Jesus Christ or His Apostles say divorce ends a marriage?
The Lord Jesus Christ has much to offer the humble heart...

The core truth: In today's world, anyone can get a divorce, however, the only divorce that the Lord Jesus Christ allows (and yes, requires) is to leave a marriage where one (or both) of the spouses are already divorced from their very own husband or wife. That kind of re-marriage is called fornication (KJV) or sexual immorality (NIV).   
See Matthew 19, Mark 6, and 1 Corinthians 7:2. 

Divorce ends a marriage that is only joined civilly and not by God because joining that marriage would be sinful.  Divorce only ends that kind of marriage; a marriage that is sexually immoral (fornication). A marriage of sexual immorality or fornication isn't joined by God because one or both spouses are already "one flesh" and bound with another still living (and divorced from) spouse.  Since God will not join a sinful re-marriage, a marriage of sexual immorality or fornication is only a civil contract that must be divorced from to honor the original marriage bond that remains applicable until death. 

"But I say unto you, That whosoever shall put away his wife, saving for the cause of fornication, causeth her to commit adultery..." Matthew 5:32 (KJV) "But I tell you that anyone who divorces his wife, except for sexual immorality, makes her the victim of adultery, and anyone who marries a divorced woman commits adultery." Matthew 5:32 (NIV)
Application: This identifies that "fornication" or sexual immorality is being married to another person while the spouse you were married and joined to by God, but are now divorced from, still lives. The sexually immoral marriage or "fornication" is the only marriage where divorcing or "putting away" of a spouse is permitted by the Lord Jesus Christ, since that marriage isn't joined by God.


"What therefore God hath joined together, let not man put asunder." Matthew 19:6 (KJV)
Application: This establishes that God is the Creator of the marriage HE joins. When He performs the miracle of "making the two one flesh" (because neither the husband or wife already have a living spouse He joined them to) divorce can put asunder / separate a one flesh marriage, but divorce cannot undo it. For the husband and wife that God makes one flesh, the bond is unbreakable (Genesis 2:18-25). Only if the husband or wife passes away is the "one flesh" marriage bond no longer applicable, yet still recognized. (Matthew 1:6, Romans 7:1-3, and 1 Corinthians 7:39)


*God Does Not Join All Marriages: John the Baptist was martyred for telling Herod his marriage to Herodias was unlawful. She was still the wife of, and bound to, her living husband, Philip. This proves that a civil marriage does not override God's Law:

"For Herod had laid hold on John, and bound him, and put him in prison for Herodias' sake, his brother Philip's wife. For John said unto him, It is not lawful for thee to have her." Matthew 14:3-4 (KJV)

"For Herod himself had sent forth and laid hold upon John, and bound him in prison for Herodias' sake, his brother Philip's wife: for he had married her. For John had said unto Herod, It is not lawful for thee to have thy brother's wife. " Mark 6:17-18 (KJV)

 

*Please note that being in bondage is NOT THE SAME as being bound in marriage: 

It is essential to know the difference of the bond of God’s law of marriage and bondage of a contentious “one flesh” spouse:

*Being bound in marriage:

“The wife is bound by the law as long as her husband liveth; but if her husband be dead, she is at liberty to be married to whom she will; only in the Lord.” 1 Corinthians 7:39  (KJV)


“Know ye not, brethren, (for I speak to them that know the law,) how that the law hath dominion over a man as long as he liveth? For the woman which hath an husband is bound by the law to her husband so long as he liveth; but if the husband be dead, she is loosed from the law of her husband. So then if, while her husband liveth, she be married to another man, she shall be called an adulteress: but if her husband be dead, she is free from that law; so that she is no adulteress, though she be married to another man.” Romans 7:1-3 (KJV)

 

Being in bondage:

“But if the unbelieving depart, let him depart. A brother or a sister is not under bondage in such cases: but God hath called us to peace.” 1 Corinthians 7:15 (KJV)


When an unbelieving spouse chooses to leave, the believer is not “under bondage” to forcibly prevent their departure or continue a cycle of strife. God has called the believer to peace. The verse directly above (nor any other verse) does not state that the marriage covenant itself is dissolved, for nothing ends a marriage that God has joined together, only death makes it not applicable.  Even if your spouse leaves, you can have peace in your heart from the Lord Jesus Christ as HE promises all His true followers, despite the trials or tribulations we all must endure.  Nowhere in Scripture is it written that the departure and/or divorce of your one flesh spouse “un-joins” you from your spouse or ends the covenant. Paul clarifies that the only thing that registers the marriage bond that God joins together not applicable is death of the spouse. That is why Adam and Eve are the perfect analogy for marriage, they were one flesh and bound together, from the beginning:


“And the LORD God said, It is not good that the man should be alone; I will make him an help meet for him. And out of the ground the LORD God formed every beast of the field, and every fowl of the air; and brought them unto Adam to see what he would call them: and whatsoever Adam called every living creature, that was the name thereof. And Adam gave names to all cattle, and to the fowl of the air, and to every beast of the field; but for Adam there was not found an help meet for him.  And the LORD God caused a deep sleep to fall upon Adam, and he slept: and he took one of his ribs, and closed up the flesh instead thereof;  And the rib, which the LORD God had taken from man, made he a woman, and brought her unto the man. And Adam said, This is now bone of my bones, and flesh of my flesh: she shall be called Woman, because she was taken out of Man. Therefore shall a man leave his father and his mother, and shall cleave unto his wife: and they shall be one flesh. And they were both naked, the man and his wife, and were not ashamed.  Genesis 2:18-25 (KJV)


To obey the Commandment of Jesus Christ, you can’t stop loving your spouse because they depart. For Jesus Christ said, “A new commandment I give unto you, That ye love one another; as I have loved you, that ye also love one another.  By this shall all men know that ye are my disciples, if ye have love one to another.” John 13:34-35 (KJV)


Paul further explains the Commandments of Jesus Christ, when he says; “Wives, submit yourselves unto your OWN husbands, as unto the Lord. For the husband is the head of the wife, even as Christ is the head of the church: and he is the saviour of the body. Therefore as the church is subject unto Christ, so let the wives be to their own husbands in every thing. Husbands, love your wives, even as Christ also loved the church, and gave himself for it; That he might sanctify and cleanse it with the washing of water by the word, That he might present it to himself a glorious church, not having spot, or wrinkle, or any such thing; but that it should be holy and without blemish.  So ought men to love their wives as their own bodies. He that loveth his wife loveth himself.  For no man ever yet hated his own flesh; but nourisheth and cherisheth it, even as the Lord the church:  For we are members of his body, of his flesh, and of his bones. For this cause shall a man leave his father and mother, and shall be joined unto his wife, and they two shall be one flesh. his is a great mystery: but I speak concerning Christ and the church. Nevertheless let every one of you in particular so love his wife even as himself; and the wife see that she reverence her husband. “ Ephesians 5:22-33 KJV

To understand the limits of a wife’s or husband’s liberty, one must look to the totality of Scripture. Romans confirms that the authority of the God’s marriage law remains active as long as both spouses are alive.

“Do you not know, brothers and sisters–for I am speaking to those who know the law–that the law has authority over someone only as long as that person lives? For example, by law a married woman is bound to her husband as long as he is alive, but if her husband dies, she is released from the law that binds her to him.  So then, if she has sexual relations with another man while her husband is still alive, she is called an adulteress. But if her husband dies, she is released from that law and is not an adulteress if she marries another man.” Romans 7:1-3 (NIV)


Summary: While a believer is not required to fight a spouse’s desire to separate (the bondage of conflict), they remain spiritually bound to that spouse by God. Physical departure does not equal spiritual “un-joining”; therefore, the marriage bond remains applicable until the death of a spouse.