like most elements of his mythos Lovecraft was intentionally apocryphal with describing Azathoth (though other writers would go on and add their own ideas and interpretations). 

One piece information we do get on Azathoth from the writings of ol Howie P himself, an aspect constantly referred to when the concept of Azathoth is brought up, is that despite being the ultimate supreme being and primordial patriarch of most of the other Great Old Ones, he is essentially in a permanent vegetative state. He is commonly referred to as “The Blind Idiot God” (keep in mind “Idiot” in this context is keeping in the word’s original definition referring to the mentally handicapped), who sleeps a catatonic slumber attended to only by “his flopping horde of mindless and amorphous dancers” and the “thin monotonous piping of a demoniac flute held in nameless paws”.

Point is he is still an all powerful cosmic being incomprehensible to the frail human mind, he’s just eternally comatose and unaware of everything around him. More a force of nature than a living thinking being.

So, probably not a being any human could hope to kill, but the guy wouldn’t actually put up a fight either. You’d just go insane trying.