La guillotina corta el papel marmoleado.

Because Spanish nouns have grammatical gender. Guillotina is feminine, so it takes la. Papel is masculine, so it takes el.

The article has to match the noun:

• la guillotina
• el papel

This is grammatical gender, not biological sex. Objects can be masculine or feminine just as part of the language.

Corta is the 3rd person singular present indicative of the verb cortar.

So it matches la guillotina:

• yo corto = I cut
• tú cortas = you cut
• él / ella / usted corta = he / she / you cut

Here, la guillotina corta means the subject la guillotina performs the action.

Depending on context, the present tense in Spanish can mean:

• cuts
• is cutting
• sometimes a more general does cut

In Spanish, descriptive adjectives usually come after the noun.

So:

• el papel marmoleado = the marbled paper

This is the normal order for a straightforward description. Putting the adjective before the noun is much less common here and would sound marked, literary, or unusual.

Because the adjective must agree with the noun it describes.

Papel is:

• masculine
• singular

So the adjective must also be masculine singular:

• papel marmoleado

Compare:

• el papel marmoleado = masculine singular
• la hoja marmoleada = feminine singular
• los papeles marmoleados = masculine plural
• las hojas marmoleadas = feminine plural

It is functioning here as an adjective, but it comes from a past participle.

Many Spanish adjectives are past participles used adjectivally. In this sentence, marmoleado describes the paper’s appearance or finish.

So grammatically in this sentence, you can think of it as a normal describing word that still follows the usual agreement rules.

Because el papel marmoleado is the direct object of corta, and direct objects in Spanish usually do not take a preposition.

You only get the personal a with certain direct objects, mainly specific people (and sometimes animals or personified things).

Compare:

• Corta el papel marmoleado. = no a, because it is a thing
• Veo a María. = a appears, because María is a person

Yes, Spanish often omits the subject when it is understood:

• Corta el papel marmoleado.

However, without context, that sentence could mean:

• he/she/it cuts the marbled paper
• you (formal) cut the marbled paper

So including la guillotina makes the subject completely clear.

A Spain pronunciation would usually be close to:

gui-yo-TI-na

A few useful points:

• In gui, the u is silent, so it sounds like gi
• ll in most of Spain is pronounced like a y sound
• The stress falls on ti

A rough full pronunciation of the sentence is:

la gi-yo-TI-na KOR-ta el pa-PEL mar-mo-le-A-do

If you want it a bit more precisely:

• guillotina ≈ giyoTIna
• corta ≈ KOR-ta
• papel ≈ paPEL
• marmoleado ≈ mar-mo-le-A-do

Yes. Corta can also be an adjective meaning short in the feminine singular form:

• una falda corta = a short skirt

But in this sentence, it is clearly a verb, because it sits between the subject and the object:

• La guillotina = subject
• corta = verb
• el papel marmoleado = direct object

So here it can only be understood as cuts.

They are used because the sentence refers to specific nouns:

• la guillotina
• el papel marmoleado

In normal Spanish, the articles sound natural here. If you removed them:

• Guillotina corta papel marmoleado

that would sound incomplete, unnatural, or like very compressed note-taking or a headline.

So in ordinary sentences, keeping la and el is the normal choice.