"No, I can't help you," he said with his voice down.

[teacherjapan]

I wrote this sentence. Is this correct?

“No, I can’t help you,” he said with his voice down.

 

[teechar]

I wrote this sentence. Is this correct?

That sounds as if you're asking us to confirm whether you were the person who wrote it! Say: "I wrote this sentence. Is it correct?"

“No, I can’t help you,” he said with his voice down.

I would say "he said, in a low voice".

 

[emsr2d2]

We use "down" in the imperative "Keep your voice down" but otherwise we use "a low voice" or "a quiet voice".

 

[teechar]

We use "down" in the imperative "Keep your voice down"

It's not exclusive to the imperative. Keeping one's voice down can work in all sorts of sentences.
My neighbours are usually loud, but they kept their voices down last night.

 

[emsr2d2]

@teacherjapan Note that I have changed your thread title. Titles must be unique, relevant only to their thread and contain some/all of the words/phrases/sentences you're asking us to look at. Your original title ("Is this sentence correct?") did not fulfil any of those criteria.