Θέλω το μπλε, όχι το κόκκινο.

Because in this sentence the colors are being used like nouns: the blue one and the red one.

Greek often uses the definite article this way with adjectives when the noun is understood from context. So:

• το μπλε = the blue one / the blue thing
• το κόκκινο = the red one / the red thing

In English, we often leave one out in casual speech too: I want the blue, not the red. Greek does the same kind of thing very naturally.

They behave a little differently grammatically.

• μπλε is usually indeclinable in Modern Greek. That means it often stays the same in different genders and cases.
• κόκκινο comes from the adjective κόκκινος, -η, -ο and changes form to match gender, number, and case.

Here both are used with το, which is neuter singular, so:

• το μπλε
• το κόκκινο

If the noun were feminine or masculine, κόκκινος would change, while μπλε usually would not:

• η κόκκινη τσάντα = the red bag
• ο κόκκινος καναπές = the red sofa
• η μπλε τσάντα, ο μπλε καναπές

When Greek leaves out the noun and just says the blue one or the red one, the neuter singular is very commonly used, especially when referring to an object in a general way.

So το μπλε and το κόκκινο are natural ways to say:

• the blue one
• the red one

Sometimes the gender can match an implied noun if that noun is clear from context, but in sentences like this, the neuter is very common and natural.

Θέλω means I want.

It is the 1st person singular form of the verb θέλω.

So:

• Θέλω = I want
• Θέλω το μπλε = I want the blue one

This is a very common everyday verb in Greek.

Όχι means no or not, depending on context.

In this sentence, it means not:

• Θέλω το μπλε, όχι το κόκκινο.
• I want the blue one, not the red one.

It is being used to reject the second option.

You can also use όχι by itself:

• Όχι. = No.

Yes. If you want to be more explicit, you can include the noun:

• Θέλω το μπλε πουκάμισο, όχι το κόκκινο.
• I want the blue shirt, not the red one.

Or even:

• Θέλω το μπλε πουκάμισο, όχι το κόκκινο πουκάμισο.

But Greek often avoids repeating the noun when it is obvious from context, just like English does.

A rough pronunciation guide is:

• Θέλω ≈ THE-lo
• το ≈ to
• μπλε ≈ ble
• όχι ≈ O-hi (with h like a soft breathy sound)
• κόκκινο ≈ KO-ki-no

A more connected version would sound roughly like:

THE-lo to ble, O-hi to KO-ki-no.

A few useful notes:

• θ sounds like th in think
• μπ at the start of a word usually sounds like b
• the accented syllables are Θέ-, ό-, and κό-

The comma separates the two contrasted choices:

• το μπλε
• όχι το κόκκινο

It helps show the pause and the contrast: the blue one, not the red one.

In English we also often use a comma in this kind of contrastive sentence.

The given order is the most natural for a simple statement:

• Θέλω το μπλε, όχι το κόκκινο.

Greek does allow some flexibility, but changing the order can shift emphasis. For example:

• Το μπλε θέλω, όχι το κόκκινο.

This puts stronger emphasis on το μπλε: It’s the blue one I want, not the red one.

So the original sentence is the neutral, everyday way to say it.

Usually they function as adjectives, but in sentences like this they are acting like adjective-based noun phrases:

• το μπλε = literally something like the blue
• το κόκκινο = the red

This is very common in Greek. English does something similar in expressions like:

• the rich
• the poor
• the blue one

So the colors are still basically adjectival words, but here they are standing in for a noun that is understood from context.