J’en arrache du tissu is better because that means you tear off fabric from the jacket, i.e. fabric that is part of it.

You can also say: je lui arrache du tissu with the same meaning but j’y arrache du tissu means, assuming this is formal French, that there is a place where you tear off some fabric without implying anything about the jacket.

In relaxed colloquial French, y can be used the way you did.

Ce livre, j’en arrache une page. more formal

Ce livre, je lui arrache une page. common

Ce livre, j’y arrache une page. colloquial, spoken French only

Let’s have some fun with this. Imagine a stage setting in a theater. Let’s imagine that the fabric is sewn together in little squares and stapled to the frame of a slat.

1. • J’ai arraché le tissu à un des coins du cadre.

• I tore the fabric off one of the frame’s corners.

2. • J’y ai arraché le tissu. [ y goes to corner where I tore it off due to the à.]

• I tore it off there. [at/from the corner]

3. • J’en ai arraché à cause des taches.

• I tore some of it [some of the fabric] off because of the stains. [en=some of it]

4. • J’y en ai arraché pour le remplacer. [notice:both y and en]

• I tore some of it off there to replace it [so it could be replaced].

So, going back over this: the "y" means "there" [at that spot] and the "en" means some of it, not all of it.

Compare:
5) – J’aurais pu tout arracher mais cela aurait donné plus de travail. [tout versus en]

• I could have torn it all off but that would have meant more work.