There's no sense in arguing with him about it now; he's already made up his mind.

sense 在这里是名词，意思是"意义、道理"，指某件事是否有合理性或价值。 made up his mind 是一个固定短语，由 make up（决定）和 mind（想法）组成，意思是"下定决心、做出决定"。