分 (divde) + 手 (hands) =分手 (break up)
In Vietnamese. “分” means "chia", “手” means “tay”. And "chia tay" means break up.
Could this also be 我跟他想分手？
That means, colloquially, that the both of you want to break up.
Is the了 particle needed here? “我想跟他分手了”？ Change of state, right?
I think that sounds more like "I've now decided I want to break up with him." to me.