Powiedz to słowo jeszcze raz.

Powiedz is the imperative form of powiedzieć, so it means say! when speaking to one person in an informal way.

It is also a perfective verb form, which fits a single complete action: say it once, say it now.

Related forms:

• powiedzcie = say! (to more than one person, or to a group informally)
• proszę powiedzieć = please say... (polite/formal)

Because Polish usually drops subject pronouns when they are obvious from the verb form.

So powiedz already tells you that the speaker is addressing you singular, informally. Adding ty is possible, but it would sound emphatic, contrastive, or sometimes irritated:

• Ty powiedz to słowo jeszcze raz.

In normal speech, the pronoun is usually left out.

This is mainly about aspect and what kind of action is being requested.

• powiedz from powiedzieć = say it once / say it as a complete act
• mów from mówić = more like speak / keep saying / be talking

In a sentence like this, Polish naturally prefers powiedz, because the speaker wants one repetition of one word.

A very common alternative is:

• Powtórz to słowo jeszcze raz.
  This means something like Repeat that word once more.

It is in the accusative singular, because it is the direct object of powiedz.

The useful thing to notice is that słowo is a neuter noun, and for many neuter nouns the nominative and accusative singular look the same.

So:

• słowo = nominative
• słowo = accusative

That is why the form does not visibly change here.

Because słowo is neuter, and the demonstrative has to agree with it in gender.

Polish uses:

• ten for masculine
• ta for feminine
• to for neuter

So:

• ten dom = this/that house
• ta książka = this/that book
• to słowo = this/that word

Since słowo is neuter, to is the correct form.

No. Polish does not have articles like a or the.

Here, to is a demonstrative, meaning this or that, depending on context. So to słowo means this word or that word, not just a generic the word in the English article sense.

You can sometimes omit to:

• Powiedz słowo jeszcze raz.

That is grammatical, but it sounds less explicitly specific. With to, the speaker is clearly pointing to a particular word.

It can mean either this word or that word. Context decides.

Polish to is often less strict than English about the this/that distinction. If you need a stronger idea of that one over there, Polish can use forms like tamto.

So in everyday conversation, to słowo may be translated as either:

• this word
• that word

depending on the situation.

Literally, jeszcze raz is something like yet one more time or once more.

In natural English, it usually corresponds to:

• again
• once more
• one more time

It is a very common Polish expression for asking someone to repeat something.

You may also see:

• znowu = again
• ponownie = again / anew / once again

But jeszcze raz is especially common in speech when asking for repetition.

Yes. Polish word order is fairly flexible, because grammar is shown a lot by endings, not only by position.

The given sentence:

• Powiedz to słowo jeszcze raz.

is a very natural, neutral order.

Other possible orders include:

• Powiedz jeszcze raz to słowo.
• Jeszcze raz powiedz to słowo.

These are still understandable, but they shift emphasis a little:

• putting jeszcze raz earlier highlights the repetition more
• keeping to słowo right after the verb can feel more neutral

Yes, you can.

• Powiedz mi to słowo jeszcze raz.

Here mi means to me.

Without mi, the sentence simply means say that word again. The listener may still understand that they are saying it to you, but mi makes that explicit.

A rough English-style approximation is:

PO-vyetss to SWO-vo YESH-che rass

A few important sound notes:

• w sounds like English v
• ł sounds like English w
• powiedz ends in a sound closer to -ts than English -dz at the end
• słowo is roughly SWO-vo
• jeszcze has the cluster szcz, which is stronger than simple English sh
• final z in raz is devoiced, so it sounds closer to s

So:

• powiedz ≈ PO-vyetss
• słowo ≈ SWO-vo
• jeszcze raz ≈ YESH-che rass

If you are speaking to several people informally:

• Powiedzcie to słowo jeszcze raz.

If you want to be polite/formal to one person:

• Proszę powiedzieć to słowo jeszcze raz.
• Niech pan powie to słowo jeszcze raz.
• Niech pani powie to słowo jeszcze raz.

So the original sentence is best understood as an informal singular request.