Mit der Küchenrolle wische ich Wasser vom Tisch, damit nichts klebt.

Küchenrolle usually means a roll of kitchen paper / paper towels. In this sentence, mit der Küchenrolle means using a paper towel or with the paper towel.

In everyday German, this is a very normal way to say it. English often prefers paper towel in the singular as a material-like noun, while German uses Küchenrolle for the roll itself.

Because mit always takes the dative case.

• die Küchenrolle = nominative
• der Küchenrolle = dative

So:

• mit der Küchenrolle = with the paper towel

This is a very common pattern:

• mit dem Messer = with the knife
• mit der Hand = with the hand
• mit einem Tuch = with a cloth

Because the sentence starts with Mit der Küchenrolle, and in a German main clause, the finite verb must be in second position.

So the structure is:

• Mit der Küchenrolle = first element
• wische = verb in second position
• ich = subject after the verb

This is called verb-second word order.

You could also say:

• Ich wische mit der Küchenrolle Wasser vom Tisch, damit nichts klebt.

That is also correct, but the original sentence puts emphasis on how the person is wiping: with the paper towel.

Because German often leaves out the article with uncountable substances when speaking in a general sense.

So:

• ich wische Wasser vom Tisch = I wipe water off the table

This sounds natural because we are not talking about a specific, clearly identified amount of water. We just mean some water.

You could say das Wasser in a different context, especially if it is specific:

• Ich wische das Wasser vom Tisch.
  = I wipe the water off the table.

Both are possible, but without the article sounds very natural here.

vom is a contraction of von dem.

• von dem Tisch → vom Tisch

Here it means from the table or more naturally in English, off the table.

This contraction is extremely common:

• vom Haus = from the house
• vom Arzt = from the doctor
• vom Tisch = from the table

Because von takes the dative case, and Tisch is masculine:

• nominative: der Tisch
• accusative: den Tisch
• dative: dem Tisch

So:

• von dem Tisch = from the table
• contracted: vom Tisch

That is why you do not get den Tisch here.

The verb is wischen = to wipe.

In this sentence, the thing being wiped is:

• Wasser = direct object

And the place it is being removed from is:

• vom Tisch = from the table

So:

• Wasser vom Tisch wischen = to wipe water off the table

This is slightly different from:

• den Tisch wischen = to wipe the table

Compare:

• Ich wische den Tisch. = I wipe the table.
• Ich wische Wasser vom Tisch. = I wipe water off the table.

damit introduces a purpose clause. It means so that or in order that.

So:

• damit nichts klebt = so that nothing sticks / so that nothing is sticky

The speaker is explaining why they are wiping the water away.

This is a very common structure:

• Ich lerne, damit ich die Prüfung bestehe.
  = I study so that I pass the exam.
• Sie spricht leise, damit das Baby schläft.
  = She speaks quietly so that the baby sleeps.

Because damit starts a subordinate clause, and in German subordinate clauses, the conjugated verb goes to the end.

Main clause:

• Ich wische Wasser vom Tisch.

Subordinate clause:

• damit nichts klebt

So the pattern is:

• damit + subject + ... + verb

Examples:

• damit ich es verstehe
• damit er kommen kann
• damit nichts klebt

This verb-final order is one of the most important grammar patterns in German.

Because nichts means nothing, while nicht means not.

So:

• nichts klebt = nothing is sticky / nothing sticks
• nicht klebt would be incomplete or wrong here

You use nichts when it itself is the subject or object:

• Nichts passiert. = Nothing happens.
• Ich sehe nichts. = I see nothing.

Here, nichts is the subject of klebt.

The verb kleben literally means to stick or to be stuck. In this context, damit nichts klebt means something like:

• so that nothing is sticky
• so that nothing sticks
• so nothing remains sticky

It sounds natural because spilled water can leave behind sugar, juice, or other residue that makes the table sticky.

So the sentence is not saying that the water itself is gluing things down. It means the speaker is wiping the table so the surface does not end up sticky.

Not naturally in this sentence, because um ... zu is usually used when the subject of both clauses is the same and the second clause has no separate subject.

For example:

• Ich wische das Wasser weg, um den Tisch sauber zu halten.
  = I wipe the water away to keep the table clean.

But in the original sentence, the second clause has its own subject:

• nichts klebt

Because there is a subject there, damit is the normal choice:

• ..., damit nichts klebt.

Yes, it sounds natural and idiomatic.

A native speaker might also say similar versions such as:

• Mit der Küchenrolle wische ich das Wasser vom Tisch, damit nichts klebt.
• Ich wische das Wasser mit der Küchenrolle vom Tisch.
• Ich wische den Tisch trocken, damit nichts klebt.

The original sentence is perfectly normal. It simply begins with Mit der Küchenrolle to foreground the tool being used.