"Yes, I know you want to kill me, so don't contact me, don't come near my home at such and such address, or my work at such and such address, or you will be guilty of a minor misdemeanor!" Right.... that's a good idea...
If the harasser could get carried away in an argument and start beating, but didn't leave the house planning to kill, then restraining orders can limit the time the harasser is around you and limit the time before they 'blow their cool'. When the harasser breaks the restraining order and comes near you "just to talk, I promise", you can get the police involved straight away, and the harasser can be hauled off before they lose their cool.
If someone is out to kill you, go hide with relatives, some ways not too close. Don't serve them with a restraining order.
Define not too close. My closest relatives are over 200 miles away. Am I expected to quit my job? Take my children (If I had them) out of school? For how long?
This person may know exactly who all your relatives are and where they live, thus know exactly where to find you anyways.
Some of the people replying here clearly have no experience with stalking or domestic violence... They are much more scary than you can imagine.