“Ne manger pas” is never said; that’s simply a fact of usage; this succession of grammatical fonctions is however correct for the imperative: “Ne mangez pas!”.

grammar correct is

ne mangez pas?

ne mangez pas (cette pomme) : don’t eat (that apple)

Examples
“Ne mangez pas ce pauvre stagiaire.”

There are a few different ways to say that people shouldn’t eat, and it depends on the context.

1. Negative infinitive: « Ne pas manger »

As aCOWst said, the infinitive comes last in series like this, leading to the “ne pas” with nothing between it that sounds so odd to learners of French. This formula would be used in directions printed but not aimed at anyone in particular, such as how to use a cake mix.

2. Negative imperative: « Ne mangez pas » or « Ne mange pas »

This is the form you were expecting since it looks more like normal verbal grammar. This would be used more often when directly addressing one person or a group of people.

3. Periphrasis: « Interdit de manger » or « Défense de manger »

For various reasons, you might choose to say this indirectly. For example, if « Ne pas manger » is the equivalent of “Do not eat”, then « Défense de manger » might mean “No eating” or “Eating is not allowed”.

4. Modals: « Il ne faut pas manger » or « Vous ne devez pas manger » (among others)

These are similar to the negative imperative, but softer. It’s a bit like combining the indirect wording with the imperative. You want to address someone specific but to take a tone of informing, not commanding.