Once the carpet fibers have absorbed the stain, you can only bleach it to get it out. HOWEVER, you now must get a matching color. The problem is that the surrounding carpet is already 'worn' and you won't get an 'invisible match' to boot.
As for replacing the damaged area, yes, that can be done. However, your patch-carpet will be brand new and the surrounding area will be worn. Again, it won't match very well so you will notice it.
Well, what are you left to do? Patch it anyway or get a new carpet OR cover it with furniture or a rug or something.