Har De en saks, så jeg kan klippe billedet ud?

Because this is a yes/no question.

In Danish, yes/no questions usually have the finite verb first and the subject second:

• Statement: De har en saks.
• Question: Har De en saks?

So Har De ...? is the normal question pattern, just like English Do you have ...?

De means you in a formal/polite way.

So the speaker is addressing someone respectfully, not casually. In everyday modern Danish, people usually say du instead, but De is still correct in formal situations.

The capital letter shows that it is the formal pronoun De.

This helps distinguish it from de, which usually means they or those.

So:

• De = formal you
• de = they / those

It can be either, depending on context.

Historically, De was used as a polite form and could refer to one person or more than one person. In this sentence, it most likely means one person being addressed politely.

In modern everyday Danish:

• du = singular informal you
• I = plural informal you
• De = formal you (less common now)

Much less than before.

Modern Danish usually prefers du, even in many situations where English might still use a polite tone. De can sound:

• formal
• old-fashioned
• distant
• extra respectful

So the sentence is correct, but a more everyday version would usually be:

• Har du en saks, så jeg kan klippe billedet ud?

Because Danish treats saks as a singular count noun.

So Danish says:

• en saks = literally a scissors, but naturally translated as a pair of scissors

This is just a vocabulary difference between the languages.

Also note:

• en saks = one pair of scissors
• plural: sakse = several pairs of scissors

Because billedet means the picture, while et billede means a picture.

Danish usually puts the definite article at the end of the noun:

• et billede = a picture
• billedet = the picture

So the speaker is referring to a specific picture, not just any picture.

Here så means so that.

It introduces the purpose of asking for the scissors:

• Har De en saks, så jeg kan klippe billedet ud?

In other words, the speaker wants the scissors in order to cut the picture out.

Because here så is introducing a subordinate clause meaning so that.

In this kind of clause, Danish keeps the normal subordinate-clause order:

• så jeg kan ...

If så meant something more like so / then and started a new main clause, you would get main-clause word order:

• ..., så kan jeg ...

So there is a real difference:

• så jeg kan ... = so that I can ...
• så kan jeg ... = then I can ...

Because kan is a modal verb, and modal verbs in Danish take the bare infinitive.

So you say:

• jeg kan klippe
• not jeg kan at klippe

This is similar to English:

• I can cut
• not I can to cut

Other Danish modal verbs work the same way, for example vil, skal, må, and bør.

klippe ... ud means to cut out.

The word ud is a particle that belongs with klippe. Together they form the meaning cut out, not just cut.

In Danish, these particles are often separated from the main verb:

• Jeg klipper billedet ud.
• Jeg kan klippe billedet ud.

So ud comes at the end here because that is the normal word order for this kind of verb expression.

kan is the present tense of kunne, meaning can / be able to.

Here it expresses ability or possibility:

• jeg kan klippe billedet ud = I can cut the picture out

It makes the sentence sound natural and polite: the speaker is asking for the scissors so that they are able to do the action.

It is correct, but whether it is strictly necessary depends on the comma style being used.

Danish allows variation here because many writers use an optional start comma before subordinate clauses. So you may see both:

• Har De en saks, så jeg kan klippe billedet ud?
• Har De en saks så jeg kan klippe billedet ud?

The version with the comma is very common and easy to read.

Most often, you would use du instead of De:

• Har du en saks, så jeg kan klippe billedet ud?

You might also hear people split it into two shorter sentences, which can sound even more natural in speech:

• Har du en saks? Jeg skal klippe billedet ud.

So the original sentence is grammatical, but it sounds more formal than what most Danes would usually say in everyday conversation.