If you cut the head of a cabbage off, bu leave the rest of the plant undisturbed it will form new heads although they will be much smaller. The part of Broccoli that we harvest are the flowers, so if you keep them cut they should continue producing although those too will be smaller and smaller. I have heard that you can cut Brussels Sprouts down and allow them to regrow also although I have not tried that.
These are really cool weather crops so you may want to pull them out and plant somethign more suitable for this hot weather and follow up later with a fall crop of these.

I think it would be a good idea to try this question over on the Vegetable Forum where there are people who will know your conditions. I am very dubious about cutting down the Brussels sprouts because in my climate they have a very long growing season. Sow in March, plant out May/June and harvest Oct - February depending on variety. So I really doubt you can start from scratch now and get Brussels sprouts before the winter. I have never heard of cutting them down and can see no reason for it. You say the cabbage and sprouts look pretty good so why would you want to get rid of them? You'd be putting them back by months. They are biennials and if they survive the winter they will bolt next spring. You can tell they've bolted because they will have large bunches of yellow flowers.