Have a face that would stop a clock means to have a very ugly face and be extremely unattractive.
Having a face that would stop a clock always used to mean ugly and not beautiful and it sounds dated although it is still very understandable.
When someone says that someone else has a face that would stop a clock it implies that the person's appearance is so unpleasant or startling that it could theoretically halt the movement of a clock's mechanism.
The phrase a face that would stop a clock is often used humorously or unkindly to someone to describe a persons appearance being ugly and unattractive.
The phrase of have a face that would stop a clock is thought to be from the early 20th century, with the idea being that the face is so shocking that it would cause the mechanism of a clock to fail.
It's mainly associated with unattractiveness, although some people interpret it as being a way of saying that someone once had a strikingly beautiful face.