This is a British phase and is used in the past tense, it means that one beat-up another, however it is also used to descirbe a single yet dramatic hit.
"This chav was all up in Dean's face, so he twatted him, right between the eyes"
Gladys severely twatted her love rival and left her for dead
To be under the influence of particular substances. E.g. Alcohol & drugs
"I was so twatted last night"
The passed tense of tweetting, using twitter
Have you ever used the site twitter?
why yes I have twatted.
being very drunk
ive got the worst hangover ever!, can't belove i got so twatted last night