While the answer by @marcellothearcane is correct in that the leaving off a portion of the quote would be termed ellipsis, there's another portion of the construction that the two share (which rhyming slang doesn't).
I'm specifically referring to the wordplay part, e.g. where "to leave" as in "to depart" is put in the same context as "to produce new plant leaves" and "to split" as in "to depart" is put in the same context as "the dessert banana split".
This would be an example of zeugma:
zeugma (n): A figure of speech in which a word applies to two others in different senses (e.g. John and his driving licence expired last week). (Oxford Dictionaries)
This is also sometimes called syllepsis
syllepsis (n) A figure of speech in which a word is applied to two others of which it grammatically suits only one (e.g. neither they nor it is working). (Oxford Dictionaries)
The Wikipedia page on zeugma and syllepsis attempts to classify and clarify the different types of zeugma and syllepsis, as different sources draw slightly different distinctions between the two. They all share the characteristic, though, of a parallel construction where the two parts don't quite match up.
(I am unaware of a specific term that combines both the concept of ellipsis and zeugma in this way.)