The warrior jumps on an enemy, swinging an ax.

So is it a nonessential phrase? or a present participle phrase that acts as an adverb?

1. A Present Participle Phrase Acting as an Adverb
It modifies the verb “jumps” by describing how the warrior jumps (adverb of manner).

Answers: “How does the warrior jump?” → While swinging an ax.

Structurally, it’s a participial phrase headed by the present participle (“swinging”).

2. A Nonessential Phrase
It’s optional (the sentence works without it: “The warrior jumps on an enemy.”).

It’s set off by a comma, which signals it’s nonrestrictive (adds extra detail but isn’t required for grammar or core meaning).

Why It’s Both
Grammatical function: Adverbial (modifies the verb).

Punctuation/status: Nonessential (removable without breaking the sentence).

Compare to Essential (Restrictive) Participial Phrases
If the phrase were essential, it would define the subject and lack commas:

“The warrior swinging an ax (not a sword) jumps on an enemy.”

Here, “swinging an ax” specifies which warrior, making it essential.

Key Takeaway
Your original sentence uses “swinging an ax” as:

Adverbial: Modifying “jumps” (answering how).

Nonessential: Offset by a comma, adding extra detail.

This dual role is common! Many adverbial participle phrases are nonessential because they describe rather than restrict.