Мне стыдно за мои слова, и я ещё раз прошу принять моё извинение.

Because Russian often expresses feelings like стыдно with the person in the dative case.

So мне стыдно literally works like to me, it is shameful/embarrassing, but in natural English we say I am ashamed.

This is a very common Russian pattern:

• мне грустно = I am sad
• мне холодно = I am cold
• мне стыдно = I am ashamed / I feel ashamed

So even though English uses I, Russian uses мне here.

Стыдно is not a normal adjective here. It is a predicative word or category-of-state word: a word used to describe someone’s state or feeling in an impersonal construction.

That is why the sentence does not need a normal subject like я plus a verb like am.

Also, Russian usually omits the present-tense verb to be, so:

• Мне стыдно literally has no separate word for am
• but it still means I am ashamed

After стыдно, Russian often uses за + accusative to say what someone feels ashamed of.

So:

• стыдно за слова = ashamed of one’s words
• стыдно за ошибку = ashamed of one’s mistake
• стыдно за поведение = ashamed of one’s behavior

Here за мои слова means for my words / because of my words / about what I said.

Yes, свои слова is also possible, and many native speakers would actually find it more idiomatic in this context.

The difference is roughly:

• мои слова = my words, with a little more emphasis or contrast
• свои слова = one’s own words, the more reflexive, self-referential option

So:

• Мне стыдно за мои слова is grammatical
• Мне стыдно за свои слова is also grammatical and very natural

Using мои can sound slightly more explicit or emphatic.

Literally, слова means words, plural. But in Russian, just like in English, plural words can refer more broadly to what someone said.

So Мне стыдно за мои слова can mean:

• I am ashamed of my words
• I am ashamed of what I said

It does not have to refer to individual separate words in a narrow sense.

Here ещё раз means once again or one more time.

So:

• я ещё раз прошу = I ask once again / I ask once more

This is a very common expression. The word ещё can mean different things depending on context, such as still, more, or again. In ещё раз, it clearly means one more time.

Прошу means I ask or I request. It is followed here by the infinitive принять, meaning to accept.

So the structure is:

я прошу принять моё извинение
= I ask [you] to accept my apology

This is a common Russian pattern:

• прошу подождать = I ask you to wait
• прошу ответить = I ask you to answer
• прошу принять извинение = I ask you to accept the apology

It is omitted because it is understood from the context.

The full version could be:

• я ещё раз прошу вас принять моё извинение

But Russian often leaves out words that are obvious. In a sentence like this, the listener already knows they are the one being addressed, so вас is not necessary.

Omitting it sounds natural and slightly smoother, especially in formal language.

Because принять is perfective, and here the speaker is asking for one complete act: please accept my apology.

Compare:

• принять = to accept, as a completed act
• принимать = to be accepting / to accept in a repeated or ongoing way

In this sentence, the perfective verb fits because the speaker wants a single, definite result.

Both are possible.

• моё извинение = my apology
• мои извинения = my apologies

In Russian, the plural извинения is very common in polite formulas:

• Примите мои извинения
• Прошу принять мои извинения

The singular моё извинение is also correct, but it can sound a bit more formal, bookish, or solemn.

So the sentence is natural, but many native speakers might more readily say:

• Прошу принять мои извинения

It is in the accusative case, because it is the direct object of принять.

The verb asks: accept what?
Answer: моё извинение

For neuter inanimate nouns, the accusative singular looks the same as the nominative singular, so:

• nominative: моё извинение
• accusative: моё извинение

That is why the form does not visibly change.

Because и is joining two separate clauses:

1. Мне стыдно за мои слова
2. я ещё раз прошу принять моё извинение

Each part has its own predicate, so Russian normally uses a comma before и in this kind of compound sentence.

Yes, it is natural, but it sounds formal, polite, and somewhat elevated. It would fit well in:

• a written apology
• a serious conversation
• a formal message or letter

In everyday speech, a native speaker might choose something simpler, such as:

• Мне стыдно за свои слова.
• Прости меня.
• Извини меня, пожалуйста.
• Ещё раз прошу прощения.

So the given sentence is correct and natural, but not especially casual.