The answer is to decrease the secretion of substances from the pituitary gland that cause growth.
Gigantism is condition characterized by excessive growth. It is the consequence of over-production of growth hormone (somatotropin) in the pituitary gland. So, the effect of the drug used on patients diagnosed with gigantism must be to decrease the secretion of growth hormone in the pituitary gland. That way, there will be less of growth hormone, and the excessive growth can be stopped.