Without a doubt, losing sleep because a Mockingbird won't stop singing and chirping all night is no fun.
First, make sure it's a bird and not a squirrel. Squirrels make a rasping sound. Mockingbirds sound like birds.
Chasing the bird away may work for a short while, but it's unlikely to work permanently.
The male mockingbird has established his territory, and there is little you can do to change his mind.
Plastic Owls, hawks, and snakes will be of little help to stop the singing at night. Lethal action against the bird is illegal.
Just because you hear a chirping sound coming from the treetops at night doesn't mean it's a bird. Does it sound like this?
If so, it's a squirrel and we can stop right here as we are not talking about squirrels.
Other treetop night sounds can be from Katydids, Grasshoppers and crickets. Each can sound like a chirping bird in their own way.
Tree frogs are common in the south from east Texas to Florida and into the Carolinas. Search YouTube for their sounds.
On the other hand, if you're sure it's a bird singing, then first things first.
Most birds are protected by federal laws under the "Migratory Bird Act of 1918," as well as by state laws.
It is illegal to destroy, relocate or possess birds, their nests or their eggs.
The only exceptions are non-native species: House Sparrow, European Starling, and Pigeon.
Trained and licensed wildlife rehabilitators who have passed a federal and/or state-administered test are permitted to care for injured or orphaned wildlife.
As a light sleeper myself, I understand the frustration one feels when mockingbirds sing at night.
Unmated males are the most likely birds to be doing the "night singing". Once mated, the singing will usually stop as they begin the process of nest building and raising young.
Finding an acceptable noise to drown out the singing is about the only thing we can do until either a mate is found, or he gives up and moves on.
I've read online of people using garden hoses and spraying the birds. It may work and it might not.
It's considered harassment and violates local, state, and Federal laws. Charges would be under your local animal cruelty ordinances. You definitely don't want that.
Learn About The Habits of Mockingbirds