Good question. Mosaic Law are the laws passed onto the Jewish people through Moses -- these are laws like the dietary laws, hygienic laws, marital laws (eating kosher, divorce from the wife, washing one's hands required before meals, etc). Divine law are the laws that still existed during the Old Covenant but continued on too as they were laws directly from God -- only worshiping God, not murdering because of the sanctity of life, the sanctity of marriage as being of a covenant of God, etc.
You'll find that we aren't bound by Mosaic law anymore as they are expressed in Romans 7:6, Hebrews 8:13 -- but most important, in the Beatitudes and the Sermon on the Mount (
Matthew 5:1-7:28) Jesus uses the phase "You have heard it said that... but I say to you..." many times. He proceeds to give a number of examples of how the new law is harder and a higher standard than the old. For example, He replaces the Mosaic Law of "eye for an eye" with "turn the other cheek." It is clear from this that Jesus is entirely prepared to replace and expand upon the Mosaic Law.