Cortamos otro pedazo.

Cortamos comes from the verb cortar (to cut).

It is the first-person plural form, so it goes with we:

• cortamos = we cut
• depending on context, it can also mean we are cutting

So the subject is we, even though Spanish does not need to say nosotros.

In Spanish, the present tense does not always have a separate form for we are cutting. Very often, the simple present covers both ideas:

• Cortamos otro pedazo = We cut another piece / We are cutting another piece

Context tells you which meaning fits.

Also, cortamos is spelled the same as the preterite form (we cut in the past). So by itself, it can potentially mean:

• we cut (present, habitual/general)
• we are cutting (present, current action)
• we cut (preterite, past completed action)

Usually the wider context makes it clear.

Spanish often leaves out subject pronouns because the verb ending already shows who is doing the action.

• cortamos already tells you it is we
• so nosotros cortamos otro pedazo is possible, but usually unnecessary

You might include nosotros for emphasis or contrast:

• Nosotros cortamos otro pedazo, no ellos = We cut another piece, not them

Because otro normally does not take un before it in standard Spanish.

So you say:

• otro pedazo = another piece

Not:

• un otro pedazo

The word otro already contains the idea of an additional one.

Because otro works directly with the noun.

• otro pedazo = another piece
• el otro pedazo = the other piece

These are different:

• otro pedazo = one more piece / a different piece
• el otro pedazo = the other piece, the remaining one

So in your sentence, otro pedazo is the normal form for another piece.

Because pedazo is a masculine noun.

• el pedazo
• otro pedazo

Adjectives and words like otro must agree with the noun in gender and number:

• otro pedazo = another piece
• otra parte = another part
• otros pedazos = other pieces

Pedazo means piece, chunk, or bit, depending on context.

It often suggests a physical piece cut or broken from something:

• un pedazo de pan = a piece of bread
• un pedazo de pastel = a piece of cake

In this sentence, otro pedazo means another piece of something already being cut.

Yes, often you can. Trozo and pedazo can both mean piece or chunk.

• Cortamos otro pedazo
• Cortamos otro trozo

Both are natural. The exact preference can depend on region, context, and personal style. In many situations, the difference is small.

Because otro normally goes before the noun in Spanish when it means another or other in this basic sense.

• otro pedazo
• otra vez
• otro día

Putting it after the noun is not the normal pattern here.

A simple pronunciation guide is:

cor-TA-mos O-tro pe-DA-tho in much of Spain
or cor-TA-mos O-tro pe-DA-so in areas that do not use the th sound

A few helpful points for Spain Spanish:

• cortamos has the stress on ta
• otro has the stress on o
• pedazo has the stress on da
• in much of Spain, z is pronounced like the th in thin

Not by itself. Cortamos is normally we cut / we are cutting / we cut (past), not let’s cut.

For let’s cut another piece, Spanish would normally use:

• Cortemos otro pedazo

That is the subjunctive form used for a let’s command.

Yes. It is a complete sentence:

• Cortamos = verb
• otro pedazo = direct object

Even though it does not say what the piece is from, Spanish often leaves that understood from context. If needed, you could expand it:

• Cortamos otro pedazo de queso = We cut another piece of cheese