Пожалуйста, отрежь мне кусок сыра.

Отрежь is the imperative singular form of отрезать, so it means cut! when speaking to one person.

• отрезать = to cut off
• отрежь = cut off! / cut!

Russian verbs change form depending on what the speaker is doing with them. Here, the speaker is making a request, so Russian uses the imperative.

Because the sentence also has пожалуйста, the command sounds like a polite request rather than a harsh order.

Отрезать literally means to cut off or to slice off something from a larger whole.

In this sentence, the idea is:

• there is a larger piece/block of cheese
• the speaker wants one piece cut from it

So отрежь мне кусок сыра is specifically about cutting off a piece, not just cutting in a general sense.

Мне is the dative case of я.

Russian uses the dative here for the person who receives something or for whose benefit the action is done. In English, this is often expressed with for me or sometimes just me:

• Отрежь мне кусок сыра = cut me a piece of cheese / cut a piece of cheese for me

So:

• я = I
• меня = me (often accusative or genitive, depending on context)
• мне = to me / for me

Here мне is correct because the speaker is the beneficiary of the action.

After a noun like кусок meaning a piece, Russian usually puts the thing being measured or divided into the genitive case.

So:

• кусок = a piece
• сыр = cheese
• сыра = of cheese

Literally, кусок сыра means a piece of cheese.

This is a very common pattern in Russian:

• чашка чая = a cup of tea
• бутылка воды = a bottle of water
• кусок хлеба = a piece of bread

So сыра is genitive singular because it depends on кусок.

Пожалуйста most often means please in requests, as in this sentence.

But it can also mean:

• you’re welcome
• here you are
• sometimes a polite go ahead

In Пожалуйста, отрежь мне кусок сыра, it clearly means please.

Yes, пожалуйста can move around.

All of these are natural:

• Пожалуйста, отрежь мне кусок сыра.
• Отрежь мне, пожалуйста, кусок сыра.
• Отрежь, пожалуйста, мне кусок сыра.

Putting it at the beginning is very common and straightforward. Moving it inside the sentence can sound a little softer or more conversational.

The meaning stays basically the same.

It is grammatically an imperative, so it is a command form, but with пожалуйста it normally sounds like a polite request.

Still, tone and context matter.

• To a friend or family member, this sounds normal and natural.
• To a stranger or in a more formal situation, Russian often prefers a more polite plural/formal imperative.

So with ты-style speech, this is polite but familiar.

You would use the plural/formal imperative:

Пожалуйста, отрежьте мне кусок сыра.

Here:

• отрежь = singular informal, used with ты
• отрежьте = plural or formal, used with вы

Russian uses the same вы form both for:

• talking to several people
• speaking politely to one person

Отрезать is a perfective verb. In requests like this, Russian often uses the perfective imperative when asking for one complete action.

So отрежь suggests:

• do this once
• complete the action
• produce the result: a piece of cheese

That fits the situation well, because the speaker wants one finished piece.

If an imperfective verb were used instead, it could sound more like focusing on the process, repetition, or general activity rather than one completed result.

The stresses are:

• пожа́луйста
• отре́жь
• мне
• кусо́к
• сы́ра

So the sentence sounds roughly like:

пожа́луйста, отре́жь мне кусо́к сы́ра

Stress is important in Russian because it is not always predictable and can change from form to form.

Yes. You can say:

Пожалуйста, отрежь кусок сыра.

That still means Please cut a piece of cheese.

Adding мне makes it clear that the piece is for the speaker:

• отрежь кусок сыра = cut a piece of cheese
• отрежь мне кусок сыра = cut me / for me a piece of cheese

So мне is not required for grammar, but it adds an important meaning.

Yes, but the meaning changes slightly.

• кусок сыра = a piece/chunk of cheese
• ломтик сыра = a slice of cheese

So if you want a flat slice, especially for bread or a sandwich, ломтик may be more precise.

If you just mean some piece cut from a larger block, кусок is very natural.

The basic order is:

Пожалуйста, отрежь мне кусок сыра.

This is natural and neutral:

• отрежь = the action
• мне = for me
• кусок сыра = what should be cut

Russian word order is more flexible than English, so other orders are possible, for example:

• Отрежь мне, пожалуйста, кусок сыра.
• Кусок сыра мне отрежь, пожалуйста.

But changing the order can shift emphasis. The original sentence is a very normal neutral way to say it.