Finish your spinach, all of it.

Literal

Spinach [obj-を] leave-[without-ずに] eat [command-なさい].

残さずに 'without leaving (any)' uses the classical negative ず + に — a fossilized form that turns a negative into an adverb of manner ('doing X so as not to Y'). The ~なさい command with a food object is the stock parental 'eat it all' admonition. Note the all-kana rendering, characteristic of writing aimed at children or informal casual text.