It slipped my mind that I had an appointment with my teacher.

我忘记了我和我的老师有约。

slip指溜走，滑动。slip one's mind表示（某人）忘记某东西,通常都是用虚主语it加slip one's mind再加that来引导出忘记的事。

It slipped my mind that I had to turn in my homework by ten.
我忘记了我必须在十点前就交作业。