Dispensationalism's long-time rival, Covenant Theology, teaches (wrongly and indefensibly, in my opinion--although I am in general a great fan) that Jesus was correcting Pharisaical distortions of Mosaic law, or perhaps clarifying misunderstandings.
Classic Dispensationalism (Left-Behind-ism) has a particularly interesting and equally indefensible position. They teach that the Sermon, while perhaps offering good advice for Christians, is actually the rule of life for the Millennial Kingdom. We read, for example:
According to both Old Testament and New Testament, righteousness and peace are the great words of the [millennial] kingdom. The Sermon on the Mount is the expansion of the personal righteousness, which is required in the [millennial] kingdom. The great words in this present dispensation [the church age] are believe and grace. Not once do these words appear in connection with the [millennial] kingdom teachings of the Sermon (Lewis Sperry Chafer, Grace the Glorious Theme, p. 164).
In His early ministry to Israel the Lord Jesus gave none of the great heavenly truths for the present Church dispensation. He but mentioned the Church, giving no explanation. Nor were these vital Church truths revealed to the Twelve.
Paul is the declarer of the Gospel of the grace of God to us - Take Romans to Philemon out of the Bible and you are bereft of Christian doctrine. For instance, if you were to take Paul’s Epistles out of the Bible, you could not find anything about the Church, or the Body of Christ; for no other Apostle even mentions the Body of Christ (W. Newell, Peter vs. Paul, p. 6).
We see then that according to classic Dispensationalism the law (rule of life) for the church comes from the Pauline epistles, not from the Lord's great sermon.
New Covenant Theology--a nascent movement primarily in Reformed Baptist circles-- has a third view: that Jesus is replacing the Mosaic law, including if not primarily the Ten Commandments, with a fuller (and final, prior to the end of human history) revelation of God's moral law. Moses' law is a type or foreshadowing of Jesus' law--much like virtually everything in the Old Testament is a type of what was to come in the fullness of time.
Thus when Jesus says:
You have heard that it was said, ‘You shall not commit adultery. But I tell you that anyone who looks at a woman lustfully has already committed adultery with her in his heart."The Covenant Theologian has to argue, absurdly, that Jesus is "correcting" some manner of bad teaching of Moses' law, when in fact Jesus quotes the exact words of the commandment and then contrasts his teaching against the exact words. The dispensationalist must argue that this teaching is not intended for the church, but the inhabitants of a future millennial kingdom. The New Covenant Theologian has the cleanest explanation: Jesus is not saying what was taught before was bad, but what he is offering now is new and better--befitting a new and better covenant and a new and better priesthood.