If I leave my restaurant server a negative tip, should I expect them to pay me?

No. dont do this. If you were upset with your service, just tip the waiter a normal amount and leave a bad review on yelp. Unless the server was legit being rude to you, leave it alone. They're earning minimum wage, probably understaffed and poorly treated, and just trying to get by. If they were legitimately bad, rude etc then speak to the manager.

It would be nice 

Are you one of those ratchet mofos  tryna earn money w/out workin? Answer: Nah sh1t aint work like that, homie.

It is question like this that will make people spit in your food, steal your card number when they ring you up.  It will also make girls dump you when you take them out and they see you treat strangers like slaves.

yes,bravo,it was nice action,if it is but having a reason.

Why should they an why. Do you do it, Leave them alone

You should expect to be publicly named and shamed. Waitstaff talk to each other (at other restaurants). Bad tippers like you are quite literally kept in a log. Don't like tipping? Eat at quick service/fast food/self serve places, get takeaway or learn to cook.

Well, if you felt the service and or food was that bad, you should talk to the manager about a discount but you should still leave something for the server even if they didn't exceed your expectations. 

oh he will pay you alright

your food will be full of spit before he servs you so you will be paid in full

How do you leave a negative tip