Considering this sentence :

Je joue de la guitare.

De la is a partitive article. Is is used for sports and music instruments (check out the link for some examples – sentences and negative form !).

Additionally to what the article says, the right way to build the negative form actually depends on what you are going to answer.

1. You are not playing the guitar (as a habit, you don’t know how to play the guitar), or you are not playing the guitar at the moment you’re speaking. De :

Je ne joue pas de guitare.

Indeed, the article la disappears !

2. You are not playing the guitar, but you are playing the violin !

Je ne joue pas de la guitare, je joue du violon !

On that particular case, you want to keep the la.

While the rule is to drop the article in the negative forms, musical instruments are an exception so the correct sentence is always:

Je ne joue pas de la guitare.

which is the negation of

Je joue de la guitare.

With a different verb, that would be:

Je vends une guitare/des guitares (unlikely je vends de la guitare unless an informal statement by a wholesaler)

and their negation would be;

Je ne vends pas de guitare.

Reference: Académie Française:

N.B. : Il en va différemment de jouer de suivi du nom d’un instrument de musique : l’instrument sera toujours introduit par un déterminant : Je joue (ne joue pas) du piano ; Je joue (ne joue pas) de l’orgue ; Je joue (ne joue pas) des castagnettes, de la clarinette.