Como no me descuelgues el teléfono, te dejaré un mensaje en el contestador.

At the beginning of a sentence, como no + subjunctive can introduce a warning or threat, meaning if you don’t...

So here:

Como no me descuelgues el teléfono...
= If you don’t pick up the phone when I call...

It has no accent because this como is a conjunction.
Cómo with an accent means how in questions or exclamations.

Compare:

• ¿Cómo estás? = How are you?
• Como no vengas, me voy. = If you don’t come, I’m leaving.

Because this structure uses the present subjunctive:

como no + subjunctive

So Spanish says:

• Como no me descuelgues... not
• Como no me descuelgas...

The verb is descolgar. It is a stem-changing verb, so the o changes to ue in stressed forms:

• tú descuelgas = indicative
• tú descuelgues = subjunctive

Here the subjunctive is required by the construction; it does not mean the action is especially doubtful or unreal. It is just the normal grammar after this kind of como no warning.

Literally, it means to unhook the phone. This comes from older landline phones, where you physically lifted the receiver off the hook.

In modern Spanish, it simply means:

• to answer the phone
• to pick up the phone

So no me descuelgues el teléfono means don’t fail to pick up when I call.

Important: it does not mean to hang up.
To hang up is colgar.

They are object pronouns.

• me descuelgues el teléfono = you pick up the phone for me / when I call
• te dejaré un mensaje = I’ll leave you a message

So:

• me refers to the caller
• te refers to the person receiving the message

A natural English explanation of no me descuelgues el teléfono is not don’t pick me up the phone, but rather don’t fail to answer when I call you.

Often, yes.

In Spain, contestador traditionally means answering machine, but in everyday use it can also refer to voicemail in a general sense.

So:

• dejar un mensaje en el contestador = leave a message on the answering machine / voicemail

If you want a more specifically modern term, especially for mobile phones, buzón de voz is also very common.

Yes, absolutely.

You could say:

Si no me descuelgas el teléfono, te dejaré un mensaje en el contestador.

That is perfectly natural.

The difference is mainly tone:

• si no = neutral if not
• como no = more emphatic, often like a warning or strong promise

So como no... can sound a bit like:

If you don’t..., then I will...

with extra force.

Te dejaré is the simple future: I will leave you a message.

That fits very naturally after a condition like this:

• Como no me descuelgues..., te dejaré...

But in everyday speech, Spanish also often uses other forms:

• te dejo un mensaje = I’ll leave you a message
• voy a dejarte un mensaje = I’m going to leave you a message

All three are possible.
Te dejaré is just a clear, standard future form.

Because Spanish normally uses en when talking about leaving or recording something in a device, system, or place.

So:

• dejar un mensaje en el contestador
• dejar un mensaje en el buzón de voz

This corresponds to English on the answering machine / on voicemail, even though Spanish uses en.

So this is a case where Spanish and English choose different prepositions.

It is natural in Spain, but there are several common alternatives depending on tone and situation.

For example:

• Si no me coges el teléfono, te dejo un mensaje.
• Si no me contestas, te dejo un mensaje de voz.
• Si no me respondes, te dejo un mensaje.

A useful Spain-specific note: coger el teléfono is very common in Spain for pick up the phone. In some Latin American countries, coger can sound vulgar, but in Peninsular Spanish it is completely normal.