"The clock stopped."
I had the same question, but then I thought more on it - I could be wrong, but I think maybe 'sluta' would mean it is either over (has ended), or is out (like you ran out of something). So 'stanna' is used because the clock isn't gone, but has just stopped working.
Indeed, slutade would be "The clock ended".
Stanna is specifically to stop moving, or stop something you control
To force something to stop, you'd use stoppa.
No, you can only stoppa another person/thing. As in polisen stoppade honom på gatan.
Is a clock not a thing? You can stop it by removing its power source or pulling the set stem.