I get that Mutate itself won't be affected however I am looking to mutate Pheldagrif, and so have to begin playing a commander tax.
I'm hoping to at least cut back on any commander tax as it starts with (2).
I'm not sure I understand the question. If I understand correctly, you're not actually asking about mutate, but whether Goreclaw, Terror of Sal Sisma reduces commander tax?
If that is the case, the answer is yes. 601.2f tells us to determine a spell's mana cost by adding any increases (tax) then subtracting any decreases (Goreclaw). In this case, the two simply cancel each other out, at least for the first bit of commander tax.
You aren't asking this question but this statement shows a misunderstanding. Goreclaw will reduce the cost of your mutate spells as long as they have power 4 or greater. A mutate spell is a creature spell.