Do not think that I have come to abolish the Law or the Prophets; I have not come to abolish them but to fulfill them. For truly I tell you, until heaven and earth disappear, not the smallest letter, not the least stroke of a pen, will by any means disappear from the Law until everything is accomplished. Therefore anyone who sets aside one of the least of these commands and teaches others accordingly will be called least in the kingdom of heaven, but whoever practices and teaches these commands will be called great in the kingdom of heaven.
"It was said, 'WHOEVER SENDS HIS WIFE AWAY, LET HIM GIVE HER A CERTIFICATE OF DIVORCE';
but I say to you that everyone who divorces his wife, except for the reason of unchastity, makes her commit adultery; and whoever marries a divorced woman commits adultery.
(Mat 5:31-32 NASB)
Oops, there goes a jot of the law.
"Again, you have heard that the ancients were told, 'YOU SHALL NOT MAKE FALSE VOWS, BUT SHALL FULFILL YOUR VOWS TO THE LORD.' "
But I say to you, make no oath at all, either by heaven, for it is the throne of God,
(Mat 5:33-34 NASB)
There goes a tittle.
And there's still more:
"You have heard that it was said, 'AN EYE FOR AN EYE, AND A TOOTH FOR A TOOTH.' "
But I say to you, do not resist an evil person; but whoever slaps you on your right cheek, turn the other to him also.
(Mat 5:38-39 NASB)
"But go and learn what this means: 'I DESIRE COMPASSION, AND NOT SACRIFICE,' for I did not come to call the righteous, but sinners."
(Mat 9:13 NASB)
A woman who had had a hemorrhage for twelve years, and had endured much at the hands of many physicians, and had spent all that she had and was not helped at all, but rather had grown worse-- after hearing about Jesus, she came up in the crowd behind Him and touched His cloak. For she thought, "If I just touch His garments, I will get well." Immediately the flow of her blood was dried up; and she felt in her body that she was healed of her affliction.
(Mar 5:25-29 NASB)
And He *said to them, "Are you so lacking in understanding also? Do you not understand that whatever goes into the man from outside cannot defile him, because it does not go into his heart, but into his stomach, and is eliminated?" (Thus He declared all foods clean.) And He was saying, "That which proceeds out of the man, that is what defiles the man.
(Mar 7:18-20 NASB)
But when they persisted in asking Him, He straightened up, and said to them, "He who is without sin among you, let him be the first to throw a stone at her."
(Joh 8:7 NASB)
You can't just take a few verses from the beginning of the Sermon on the Mount and use that as a way to dismiss everything else. You have to read the entire sermon--and indeed, all of the Gospels-- to see that Jesus didn't interpret the law legalistically. The law is about love (Matt. 7:12, Mark 12:28-34) and when it came to things that Jesus didn't see as loving, he didn't hesitate to disregard the law on those (as the above passages demonstrate). To use the later Pauline phrase, Jesus followed the spirit of the law, rather than the letter.
I hope those that insist on following all of the Mosaic law would have followed Exodus 21:20-21 had you lived in the 1800's. To be consistent, you wouldn't have any objection to those slaves masters in the South that beat there slaves and it took a few days for them to die, correct?