Does divorce occur by the statement "I will divorce your mother," without uttering the explicit word of divorce, and knowing that the wife was in a state of purity during which he had intercourse with her?

A man's statement, "I will divorce your mother, and everything will be over between me and your mother," is merely a promise of future divorce, and divorce does not occur simply by promising it. As Shaykh al-Islam Ibn Taymiyyah stated, a promise of divorce does not take effect, nor is it obligatory or even recommended to fulfill it. Therefore, the wife remains under the man's marital bond.