The first thing that the Australians (or the British) did to try to destroy aboriginal society was to push the aborigines off the land that had been theirs. The British wanted all the best land for their own purposes. This led to violence in which the aborigines were pushed into the worst lands, thus disrupting their society in a very important way.
A second thing that was done was more clearly directed at destroying aboriginal society. This was the taking of aboriginal children from their parents. Though the extent of this practice is contested, it was carried out to some degree or other for almost 100 years. By doing this, the Australians were essentially trying to take away the aborigines' ability to pass their society on to their children.