The first feature of note is the length itself: this saying is short, extremely short in fact. Although the verbal forms are technically imperatives, the expression is really more of a condensed hypothetical: If you do not waste anything, you will not want for anything (i.e. want in the sense of to lack, to be without).
In addition to the highly compressed form, the saying is also composed with an elegant parallel structure: X not, Y not. This type of repetition is a hallmark of poetic expression, something that marks it as being different from the less orderly forms of spontaneous everyday expression.
Finally, there is also the alliteration in the words: waste - want. For more about the importance of alliteration in poetry, there is an informative article at Wikipedia. If you want to use a fancy label, you could say that this is trochaic dimeter; a trochee consists of a stressed syllable followed by an unstressed syllable, of which we have two here, hence trochaic di-meter.
For even more alliteration, consider this similar English saying, "Wilful waste makes woeful want," which again features the alliteration "waste" and "want," but which adds "wilful" and "woeful" to compound the alliteration, along with the repetition of -ful to reinforce the parallelism. And if you like poetic labels, this one is catalectic trochaic tetrameter, which is to say that it consists of four trochees minus the final unstressed syllable, therefore catalectic.
For a poster to illustrate this saying, I used a recycling image which also has the very elegant effect of a world of nature reflected in the metal recycling container! Details here: