Your analysis is more or less correct but, though trivial and "twitteresque", the sentence must be analyzed as a whole.
Removing the first interjection "mdr" which means "lol", the sentence is structured as "violet qui a dit [something] , ça me tue de rire". In this sentence, "ça" is a pronoun that refers to all the beginning, which means "violet qui a dit [something] " can be analyzed as the subject of "me tue de rire". The situation of violet saying something to Clementine is what makes the writer laugh to death.
As for a suitable translation, yes, I suppose you could say :
Lol, Violet telling Clementine to jump off the bridge while she really lost her leg, this makes me laugh to death
Please note, as you mention "Violet quand elle a dit à Clémentine..." that this would focus on Violet, not on her saying something. For example, « Violet, quand elle a dit à Clémentine... , a été vraiment méchante » (« Violet, when she told Clémentine to..., was really nasty »)