That is not a very large banyan tree. That is a moderate to smallish sized banyan tree. There is a banyan in Lahaina which covers about half a city block. There are some big ones down by the Honolulu Library & the King Kamehameha statue to compare for size. If you don't trim those things back they will eat your house then start in on the rest of the neighborhood. They get about twice that height and they continually spread out sideways, too. They are nice trees, though, they are interesting to look at and make nice shade and a good pruning program will keep them in check.

Not seeing the specific tree, it is hard to say whether cutting roots and shoots will compromise the stability of the tree or cause parts of it to die back, but I'm guessing it wouldn't. If there is a lot of concern or if the tree might endanger houses, then perhaps a commercial tree trimmer might be in order. Trying to completely get rid of a large banyan is a huge project, some neighbors several houses over have been at it for several years.

You might want to get an arborist to your house to evaluate how you can contain the tree without destabilizing it. My brother in law's neighbor had a small banyan in the back of his house. He started trimming the roots and branches to shape the tree. It looked great. Then we had a winter storm and the wind knocked the tree down onto my brother in laws house causing major damage. This could have been avoided if the tree owner had done things a little differently.

There are two tree trimming companies that I know of that have arborists - Trees of the Tropics (in Manoa valley) and the Tree People.

Good luck