Can a goiter grow back after being removed?

Yes. It is not common, but is possible. I don't recommend it myself, but some surgeons perform subtotal thyroidectomies, where they only remove a portion of the gland. This dramatically increases the chances of thyroid regrowth. However, even after a standard thyroidectomy, it very rarely possible for the thyroid to regrow from the minute amount of tissue that may be left behind.
Possibly. Some surgeons leave a small remnant of thyroid during thyroidectomy to prevent complications but it can re-enlarge. If only one side were removed then the remaining gland can continue to, get bigger.