What does Mark 12:18 mean?

The Sadducees are one sect of Judaism, like the Pharisees, Essenes, and Zealots. They believe in an extremely literal interpretation of the Old Testament and deny the existence of the spirit, judgment after death, or the afterlife. This clearly affects their lifestyle. The chief and high priests are Sadducees, as is much of the Jewish aristocracy. The Sadducees tend to be Hellenists: they welcome Greek culture. Meanwhile, the Pharisees stick to the manmade traditions of the Jewish scribes. Without a resurrection and afterlife with God to look forward to, it's reasonable the Sadducees would seek authority and wealth on earth.

Jesus hasn't been on the Sadducees' radar too much yet. Until this point, most of Jesus' controversy comes through His rejection of extra-biblical laws of the scribes and Pharisees (Mark 2:18–28; 7:7–13). Like the Herodians, the Sadducees' sole concern is Jesus' effect on the Roman rulers. If He, like others before Him, incite the people to rebellion, the Romans may send in an army to regain control. At the least, this will disrupt the Sadducees' position, and at the worst destroy Jerusalem. The Sadducees' fear will come true in AD 70, but not by Jesus' hand.

Despite divergent theologies, the Jewish ruling council, the Sanhedrin, includes members of both the Sadducees and the Pharisees. Paul uses their distinctions to good effect when he is put on trial. He declares that he has been trained as a Pharisee and shares their beliefs on the resurrection. The Sadducees and Pharisees get into such an argument over his words that the trial is halted and the Roman guard must rescue Paul from the melee (Acts 23:6–10).