Is "keep off" considered a phrasal verb, as in "keep off the grass"?

In each case keep is the verb and off is the preposition.

In "keep off the grass" there is a contraction - the object is "implied". It's actually an imperative: "Keep everything off the grass". verb-object-preposition-noun.

In "Keep your hands off her", it's a pretty straightforwards imperative. verb-object-preposition-noun.

You can tell the 'keep off' is not a phrasal verb, because it doesn't have an idomatic meaning and because the preposition off clearly refers to a noun. This is in stark contrast to "break down" (as in "break down and cry"). In the latter case, the phrase has an idiomatic meaning, and the word "down" does not link to anything else, it is intrinsic to the phrase.

In the case of "keep off the grass", "keep" is a verb, which means "continue or cause to continue in a specified condition". The specified condition is "off the grass". Clearly off is related to the grass, and not part of a phrasal verb.