Den leeren Becher wirfst du bitte in den Mülleimer, nicht auf den Tisch.

German often moves something other than the subject to the first position for emphasis or contrast.

So:

• Den leeren Becher = the empty cup
• wirfst du bitte ... = are you throwing / throw please ...

Starting with Den leeren Becher puts focus on that object, almost like:

• The empty cup — please throw that in the trash, not on the table.

This is very natural in German. The verb still stays in the second position, which is why wirfst comes right after Den leeren Becher.

A more neutral version would be:

• Du wirfst den leeren Becher bitte in den Mülleimer, nicht auf den Tisch.

Both are grammatical, but the original emphasizes what should be thrown away.

Because Becher is the direct object of the verb werfen, so it is in the accusative case.

Becher is masculine, so:

• nominative: der leere Becher
• accusative: den leeren Becher

That is why both the article and the adjective ending change:

• der → den
• leere → leeren

So the sentence is not saying the empty cup as the subject; it is saying the empty cup as the thing being thrown.

German adjectives usually take an ending when they come before a noun.

Here you have:

• den = definite article, masculine accusative
• Becher = masculine noun
• so the adjective takes the ending -en

That gives:

• den leeren Becher

Compare:

• der leere Becher = nominative
• den leeren Becher = accusative

This is a very common pattern with definite articles.

Because in a German main clause, the finite verb must be in second position.

The first position is already occupied by:

• Den leeren Becher

So the verb has to come next:

• Den leeren Becher wirfst du ...

Then the subject follows:

• ... wirfst du ...

This is one of the most important German word order rules:

• First position = one element
• Second position = conjugated verb

It is giving an instruction, but it is not the standard imperative form.

The standard imperative would be:

• Wirf den leeren Becher bitte in den Mülleimer, nicht auf den Tisch.

Your sentence uses a normal du-form statement/question structure to sound more like a spoken instruction or reminder:

• Den leeren Becher wirfst du bitte in den Mülleimer ...

This can sound:

• directive
• conversational
• slightly emphatic
• sometimes like a parent or teacher reminding someone what to do

So yes, it functions like a command, but grammatically it is not the simple imperative form.

Bitte makes the instruction sound more polite or softer.

Without bitte, the sentence can sound more direct:

• Den leeren Becher wirfst du in den Mülleimer.

With bitte:

• Den leeren Becher wirfst du bitte in den Mülleimer.

That sounds more like:

• Please throw the empty cup in the trash.

In German, bitte can appear in different places, and it often sits near the verb phrase like it does here.

These are two different prepositions because the relationships are different:

• in den Mülleimer = into the trash can
• auf den Tisch = onto the table

German chooses the preposition based on the physical idea:

• in for going inside
• auf for going onto a surface

Both in and auf are two-way prepositions, which means they can take either accusative or dative depending on meaning.

Here they both take accusative because there is movement toward a destination:

• in den Mülleimer = into the trash can
• auf den Tisch = onto the table

If you were talking about location instead of motion, you would use dative:

• im Mülleimer = in the trash can
• auf dem Tisch = on the table

Because both nouns are masculine, and both are in the accusative here.

Their dictionary forms are:

• der Mülleimer
• der Tisch

In the accusative masculine, der becomes den:

• in den Mülleimer
• auf den Tisch

This matches the idea of movement/direction after in and auf in this sentence.

Because nicht is negating that specific phrase:

• not on the table

The sentence is not negating the whole action. It is contrasting two destinations:

• in den Mülleimer
• nicht auf den Tisch

So the meaning is:

• Put it in the trash can, not on the table.

This is a very common use of nicht in German: it often comes right before the part being contrasted or denied.

It sounds like a polite but clear instruction.

Depending on context, it could sound like:

• a reminder
• a correction
• a parent/teacher-style instruction
• a practical request

Because of the fronting of Den leeren Becher and the contrast nicht auf den Tisch, it has a slightly corrective feel:

• The empty cup goes in the trash, not on the table.

So the tone is not rude, but it is definitely telling someone the correct thing to do.

Yes. A few common alternatives are:

• Wirf den leeren Becher bitte in den Mülleimer, nicht auf den Tisch.
• Den leeren Becher bitte in den Mülleimer werfen, nicht auf den Tisch.
• Bitte wirf den leeren Becher in den Mülleimer, nicht auf den Tisch.

These all mean roughly the same thing, but the tone changes a little:

• Wirf ... = straightforward imperative
• Bitte wirf ... = polite imperative
• Den leeren Becher wirfst du bitte ... = more emphatic/corrective/conversational

So the original is correct, but it is not the only natural way to say it.