to take something apart so it no longer stands: to tear down, demolish, or do away with, whether a building, a law, or a plan
At its root the verb pictures loosening something down until it collapses: pulling a structure apart stone by stone rather than blasting it out of existence. In the New Testament that image stretches across a wide range of objects. It is most at home with buildings, above all the Jerusalem temple, whose coming fall Jesus foretells and whose destruction becomes the charge thrown at him during his trial and at the cross. Paul reaches for the same picture when he calls the mortal body a tent that will one day be taken down.
The verb also moves from bricks to ideas without changing its meaning. To "tear down" a law is to set it aside so it no longer binds, which is why Jesus insists he came not to abolish the law and the prophets but to complete them. To tear down a movement is to overthrow it and bring it to nothing, the outcome Gamaliel warns the council to leave in God's hands. And Paul warns against tearing down what God has built up, whether the position he once dismantled or the work of God that a careless believer can undo over something as small as food.
The common thread is undoing what has been put together. The opposite action, building up, sits right beside it in Paul, who says that if he builds again what he once tore down he proves himself a lawbreaker. A near neighbor is the simpler verb λύω, to loosen or dissolve, which John's Gospel uses for the very same temple saying; this compound adds the sense of bringing the whole thing down.