Tu bufanda es roja, pero la mía es verde.

Because tu without an accent is the possessive adjective meaning your.

• tu bufanda = your scarf

Tú with an accent is the subject pronoun meaning you.

• Tú eres alto. = You are tall.

So in this sentence, tu is correct because it describes bufanda.

In Spanish, when you use a possessive pronoun like mine, yours, his, hers, it often comes with the definite article:

• el mío / la mía / los míos / las mías
• el tuyo / la tuya
• etc.

Here, la mía means mine, but it literally matches the omitted noun:

• Tu bufanda = your scarf
• la mía = my one / mine, where bufanda is understood

Because bufanda is feminine singular, Spanish uses la mía.

The accent mark helps distinguish it from mi:

• mi = my
• mía = mine

Compare:

• mi bufanda = my scarf
• la mía = mine

The accent is part of the correct written form of mío / mía / míos / mías.

Because roja has to agree with bufanda, which is a feminine noun.

In Spanish, adjectives usually agree in gender and number with the noun they describe.

• el libro rojo = the red book
• la bufanda roja = the red scarf

Since bufanda is feminine singular, the adjective is roja.

Not all Spanish adjectives change form for masculine and feminine.

Some adjectives, especially many that end in -e, stay the same:

• el coche verde
• la bufanda verde

So verde works for both masculine and feminine singular. It still agrees in number, though:

• el coche verde
• los coches verdes

Because it takes the feminine article:

• la bufanda

Also, nouns ending in -a are often feminine, though not always.

In this sentence, you can see the feminine gender in several places:

• tu bufanda
• roja
• la mía

They all point to bufanda being feminine singular.

It could be, but la mía is more natural because Spanish often avoids repeating a noun when it is already clear.

So these are both possible:

• Tu bufanda es roja, pero mi bufanda es verde.
• Tu bufanda es roja, pero la mía es verde.

The second one is more elegant and natural because bufanda has already been mentioned.

It agrees with the noun that is understood but omitted: bufanda.

So even though the word bufanda is not repeated, it is still mentally there:

• Tu bufanda es roja, pero la mía es verde.
• literally: Your scarf is red, but mine [scarf] is green.

Because bufanda is feminine singular, Spanish uses:

• la
  • mía

If the noun were masculine singular, it would be:

• el mío

Example:

• Tu sombrero es negro, pero el mío es marrón.

Because Spanish allows the noun to be left out when it is obvious from context.

This is very common with possessive pronouns:

• mi libro = my book
• el mío = mine

In your sentence, la mía stands for mi bufanda or more literally la bufanda mía, but the noun is omitted because it is already known.

Because there are really two complete clauses joined by pero:

1. Tu bufanda es roja
2. la mía es verde

Each clause has its own subject and verb:

• Tu bufanda
  • es
• la mía
  • es

Spanish normally keeps the verb in both parts here, just as English does in Your scarf is red, but mine is green.

Pero means but.

It connects two contrasting ideas:

• your scarf is red
• mine is green

The comma before pero is normal here because it separates two full clauses. This is very similar to English:

• Tu bufanda es roja, pero la mía es verde.
• Your scarf is red, but mine is green.

Normally, es roja is the better choice here because it describes the scarf’s color as a characteristic.

• ser is usually used for inherent qualities, identification, and descriptions like color
• estar is more often used for states or conditions

So:

• La bufanda es roja = The scarf is red

Using está roja would sound unusual in this context unless you meant something more temporary or special in context.

Then the adjectives and possessive pronoun would match a masculine noun.

Example with sombrero:

• Tu sombrero es rojo, pero el mío es verde.

Notice the changes:

• rojo instead of roja
• el mío instead of la mía

That is because sombrero is masculine singular.